Edit Profile (opens in new tab) Figalli, Alessio Compute Distance To: Compute Author ID: figalli.alessio Published as: Figalli, Alessio; Figalli, A. Further Spellings: Фигалли А Homepage: https://people.math.ethz.ch/~afigalli/ External Links: MGP · ORCID · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND · IdRef · theses.fr Awards: EMS Prize (2012) · Fields Medal (2018) Documents Indexed: 160 Publications since 2007, including 4 Books 5 Contributions as Editor · 4 Further Contributions Biographic References: 6 Publications Co-Authors: 104 Co-Authors with 143 Joint Publications 2,597 Co-Co-Authors all top 5 Co-Authors 23 single-authored 17 Ambrosio, Luigi 13 De Philippis, Guido 13 Rifford, Ludovic 11 Maggi, Francesco 7 Colombo, Maria 7 Villani, Cédric 6 Bonforte, Matteo 6 Ros-Oton, Xavier 5 Jerison, David S. 5 Kim, Young-Heon 5 Pratelli, Aldo 5 Valdinoci, Enrico 4 Caffarelli, Luis Ángel 4 Carrillo de la Plata, José Antonio 4 McCann, Robert J. 4 Serra Montolí, Joaquim 4 Shahgholian, Henrik 3 Barrios Barrera, Begoña 3 Chen, Shibing 3 Ciraolo, Giulio 3 Mooney, Connor 3 Paul, Thierry 3 Vazquez, Juan Luis 3 Wickramasekera, Neshan 2 Abbondandolo, Alberto 2 Bernot, Marc 2 Bjorland, Clayton 2 Bourgain, Jean 2 Brézis, Haïm 2 Cabré, Xavier 2 Carlen, Eric Anders 2 Crippa, Gianluca 2 Dipierro, Serena 2 Fathi, Albert 2 Friesecke, Gero 2 Giannoulis, Johannes 2 Gigli, Nicola 2 Glaudo, Federico 2 Guionnet, Alice 2 Jhaveri, Yash 2 Kang, Moon-Jin 2 Kohn, Robert Vita 2 Laurent, Thomas 2 Pelayo, Alvaro 2 Santambrogio, Filippo 2 Slepčev, Dejan 2 Spinolo, Laura V. 2 Toro, Tatiana 1 Baer, Eric 1 Bekerman, Florent 1 Bench, William 1 Braga, J. Ederson M. 1 Brendle, Simon 1 Cagnetti, Filippo 1 Chang, Sun-Yung Alice 1 Contreras, Gonzalo 1 Cordero-Erausquin, Dario 1 Cozzi, Matteo 1 da Silva, A. Belotto 1 de Franchis, Carlo 1 Del Pino, Manuel A. 1 Deproit, Laurent 1 Desvillettes, Laurent 1 Difrancesco, M. 1 Farina, Alberto 1 Fernández-Real, Xavier 1 Fusco, Nicola 1 Gallouët, Thomas O. 1 Gangbo, Wilfrid 1 Ge, Yuxin 1 Gilles, Sébastien 1 Gomes, Diogo Luís Aguiar 1 Gouëzel, Sébastien 1 Grillo, Gabriele 1 Indrei, Emanuel 1 Jerrard, Robert Leon 1 Juillet, Nicolas 1 Kim, Sunghan 1 Klein, Christian 1 Krummel, Brian 1 Ligabò, Marilena 1 Loeper, Grégoire 1 Mandorino, Vito 1 Marcon, Diego 1 Markowich, Peter Alexander 1 Millot, Vincent 1 Mingione, Giuseppe 1 Morales, Javier 1 Moreira, Diego R. 1 Morini, Massimiliano 1 Neumayer, Robin 1 Novaga, Matteo 1 Oh, Byunghyun 1 Palatucci, Giampiero 1 Palmer, Joseph 1 Parusiński, Adam 1 Patacchini, Francesco Saverio 1 Peral Alonso, Ireneo 1 Persson, Ulf A. 1 Philipowski, Robert ...and 12 more Co-Authors all top 5 Serials 13 Communications on Pure and Applied Mathematics 11 Archive for Rational Mechanics and Analysis 7 Discrete and Continuous Dynamical Systems 6 Inventiones Mathematicae 6 Journal of Functional Analysis 6 Calculus of Variations and Partial Differential Equations 4 Advances in Mathematics 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 SIAM Journal on Mathematical Analysis 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 Communications in Mathematical Physics 3 Duke Mathematical Journal 3 Journal of Differential Equations 3 Journal für die Reine und Angewandte Mathematik 3 Communications in Partial Differential Equations 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Journal of the European Mathematical Society (JEMS) 3 Oberwolfach Reports 3 Analysis & PDE 2 Acta Mathematica 2 American Journal of Mathematics 2 Gazette des Mathématiciens 2 Publications Mathématiques 2 Mathematische Annalen 2 Proceedings of the American Mathematical Society 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Geometric and Functional Analysis. GAFA 2 Bulletin of the American Mathematical Society. New Series 2 Methods and Applications of Analysis 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Lecture Notes in Mathematics 1 Israel Journal of Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Indiana University Mathematics Journal 1 Journal of Differential Geometry 1 Journal of Economic Theory 1 Mathematische Zeitschrift 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Rendiconti del Seminario Matematico della Università di Padova 1 Tohoku Mathematical Journal. Second Series 1 Transactions of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Differential and Integral Equations 1 Differential Geometry and its Applications 1 IMRN. International Mathematics Research Notices 1 The Journal of Geometric Analysis 1 Notices of the American Mathematical Society 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journal of Mathematical Sciences (New York) 1 European Mathematical Society Newsletter 1 Advances in Geometry 1 Tesi. Scuola Normale Superiore di Pisa (Nuova Serie) 1 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 Journal of Fixed Point Theory and Applications 1 Discrete and Continuous Dynamical Systems. Series S 1 Advances in Calculus of Variations 1 Cambridge Journal of Mathematics 1 Philosophical Transactions A. Royal Society of London 1 Bollettino dell’Unione Matematica Italiana 1 EMS Textbooks in Mathematics 1 Zurich Lectures in Advanced Mathematics 1 Mathematics in Engineering all top 5 Fields 83 Partial differential equations (35-XX) 72 Calculus of variations and optimal control; optimization (49-XX) 26 Differential geometry (53-XX) 14 Probability theory and stochastic processes (60-XX) 13 Dynamical systems and ergodic theory (37-XX) 13 Global analysis, analysis on manifolds (58-XX) 10 Fluid mechanics (76-XX) 8 Real functions (26-XX) 8 Measure and integration (28-XX) 8 Convex and discrete geometry (52-XX) 7 General and overarching topics; collections (00-XX) 7 Functional analysis (46-XX) 5 Operations research, mathematical programming (90-XX) 4 Quantum theory (81-XX) 4 Geophysics (86-XX) 3 History and biography (01-XX) 3 Ordinary differential equations (34-XX) 3 Statistics (62-XX) 3 Mechanics of particles and systems (70-XX) 3 Mechanics of deformable solids (74-XX) 3 Biology and other natural sciences (92-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Potential theory (31-XX) 2 Difference and functional equations (39-XX) 2 Integral equations (45-XX) 2 Operator theory (47-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Systems theory; control (93-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Manifolds and cell complexes (57-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 146 Publications have been cited 2,365 times in 1,526 Documents Cited by ▼ Year ▼ A mass transportation approach to quantitative isoperimetric inequalities. Zbl 1196.49033Figalli, A.; Maggi, F.; Pratelli, A. 129 2010 Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations. Zbl 1215.35045Carrillo, J. A.; Difrancesco, M.; Figalli, A.; Laurent, T.; Slepčev, D. 119 2011 Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients. Zbl 1169.60010Figalli, Alessio 86 2008 Isoperimetry and stability properties of balls with respect to nonlocal energies. Zbl 1312.49051Figalli, A.; Fusco, N.; Maggi, F.; Millot, V.; Morini, M. 73 2015 The Monge-Ampère equation and its applications. Zbl 1435.35003Figalli, Alessio 60 2017 Non-local gradient dependent operators. Zbl 1252.35099Bjorland, C.; Caffarelli, L.; Figalli, A. 54 2012 Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio 53 2012 Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088Caffarelli, Luis; Figalli, Alessio 51 2013 Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces. Zbl 1316.35061Barrios, Begoña; Figalli, Alessio; Valdinoci, Enrico 50 2014 The Monge-Ampère equation and its link to optimal transportation. Zbl 06377770De Philippis, Guido; Figalli, Alessio 47 2014 On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions. Zbl 1156.60036Ambrosio, Luigi; Figalli, Alessio 40 2009 Optimal transportation on non-compact manifolds. Zbl 1198.49044Fathi, Albert; Figalli, Alessio 37 2010 Stability for a GNS inequality and the log-HLS inequality, with application to the critical mass Keller-Segel equation. Zbl 1307.26027Carlen, Eric A.; Figalli, Alessio 35 2013 A refined Brunn-Minkowski inequality for convex sets. Zbl 1192.52015Figalli, A.; Maggi, F.; Pratelli, A. 34 2009 \(W^{2,1}\) regularity for solutions of the Monge-Ampère equation. Zbl 1286.35107De Philippis, Guido; Figalli, Alessio 33 2013 Asymptotics of the \(s\)-perimeter as \(s \searrow 0\). Zbl 1275.49083Dipierro, Serena; Figalli, Alessio; Palatucci, Giampiero; Valdinoci, Enrico 33 2013 The optimal partial transport problem. Zbl 1245.49059Figalli, Alessio 32 2010 Transport maps for \(\beta\)-matrix models and universality. Zbl 1330.49046Bekerman, F.; Figalli, A.; Guionnet, A. 30 2015 Mass transportation on sub-Riemannian manifolds. Zbl 1201.49048Figalli, Alessio; Rifford, Ludovic 30 2010 A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment. Zbl 1405.35206Figalli, Alessio; Kang, Moon-Jin 29 2019 \(C^{1}\) regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two. Zbl 1170.35400Figalli, Alessio; Loeper, Grégoire 28 2009 Continuity of optimal transport maps and convexity of injectivity domains on small deformations of \(\mathbb S^2\). Zbl 1175.49040Figalli, Alessio; Rifford, Ludovic 28 2009 Strongly nonlocal dislocation dynamics in crystals. Zbl 1304.35731Dipierro, Serena; Figalli, Alessio; Valdinoci, Enrico 28 2014 On the shape of liquid drops and crystals in the small mass regime. Zbl 1279.76005Figalli, A.; Maggi, F. 28 2011 A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions. Zbl 1203.35126Figalli, Alessio; Gigli, Nicola 27 2010 Nearly round spheres look convex. Zbl 1241.53031Figalli, Alessio; Rifford, Ludovic; Villani, Cedric 27 2012 Regularity and Bernstein-type results for nonlocal minimal surfaces. Zbl 1380.49060Figalli, Alessio; Valdinoci, Enrico 27 2017 Some new well-posedness results for continuity and transport equations, and applications to the chromatography system. Zbl 1222.35060Ambrosio, Luigi; Crippa, Gianluca; Figalli, Alessio; Spinolo, Laura V. 25 2009 A sharp stability result for the relative isoperimetric inequality inside convex cones. Zbl 1262.49045Figalli, A.; Indrei, E. 25 2013 Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data. Zbl 1231.35186Ambrosio, Luigi; Figalli, Alessio; Friesecke, Gero; Giannoulis, Johannes; Paul, Thierry 24 2011 Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds. Zbl 1262.58013Figalli, Alessio; Rifford, Ludovic; Villani, Cédric 24 2011 Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation. Zbl 1286.46035Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo 24 2013 When is multidimensional screening a convex program? Zbl 1282.90085Figalli, Alessio; Kim, Young-Heon; McCann, Robert J. 23 2011 On the Ma-Trudinger-Wang curvature on surfaces. Zbl 1203.53034Figalli, Alessio; Rifford, Ludovic; Villani, Cédric 22 2010 A note on interior \(W^{2,1+ \varepsilon }\) estimates for the Monge-Ampère equation. Zbl 1280.35153De Philippis, G.; Figalli, A.; Savin, O. 22 2013 Hölder continuity and injectivity of optimal maps. Zbl 1281.49037Figalli, Alessio; Kim, Young-Heon; McCann, Robert J. 22 2013 Global regularity for the free boundary in the obstacle problem for the fractional Laplacian. Zbl 1409.35044Barrios, Begoña; Figalli, Alessio; Ros-Oton, Xavier 21 2018 Existence of Eulerian solutions to the semigeostrophic equations in physical space: The 2-dimensional periodic case. Zbl 1258.35164Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio 21 2012 Geodesics in the space of measure-preserving maps and plans. Zbl 1253.76007Ambrosio, Luigi; Figalli, Alessio 21 2009 Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains. Zbl 1443.35067Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis 21 2018 A general class of free boundary problems for fully nonlinear elliptic equations. Zbl 1326.35137Figalli, Alessio; Shahgholian, Henrik 21 2014 Quantitative stability for the Brunn-Minkowski inequality. Zbl 1380.52010Figalli, Alessio; Jerison, David 21 2017 Confinement in nonlocal interaction equations. Zbl 1233.35032Carrillo, J. A.; Di Francesco, M.; Figalli, A.; Laurent, T.; Slepčev, D. 19 2012 On the Hausdorff dimension of the Mather quotient. Zbl 1172.37018Fathi, Albert; Rifford, Ludovic; Figalli, Alessio 19 2009 On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations. Zbl 1138.49031Ambrosio, Luigi; Figalli, Alessio 18 2008 Partial regularity of Brenier solutions of the Monge-Ampère equation. Zbl 1193.35087Figalli, Alessio; Kim, Young-Heon 18 2010 Regularity of optimal transport maps on multiple products of spheres. Zbl 1268.49053Figalli, Alessio; Kim, Young-Heon; McCann, Robert J. 18 2013 Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains. Zbl 1377.35259Bonforte, Matteo; Figalli, Alessio; Ros-Oton, Xavier 18 2017 Partial regularity for optimal transport maps. Zbl 1325.49051De Philippis, Guido; Figalli, Alessio 18 2015 Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature. Zbl 1411.53030Ciraolo, Giulio; Figalli, Alessio; Maggi, Francesco; Novaga, Matteo 17 2018 Total variation flow and sign fast diffusion in one dimension. Zbl 1242.35049Bonforte, Matteo; Figalli, Alessio 17 2012 BMO-type norms related to the perimeter of sets. Zbl 1352.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio 17 2016 Existence and uniqueness of maximal regular flows for non-smooth vector fields. Zbl 1348.34039Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio 17 2015 On the fine structure of the free boundary for the classical obstacle problem. Zbl 1408.35228Figalli, Alessio; Serra, Joaquim 16 2019 Regularity properties of optimal maps between nonconvex domains in the plane. Zbl 1193.35086Figalli, Alessio 16 2010 On the isoperimetric problem for radial log-convex densities. Zbl 1307.49046Figalli, A.; Maggi, F. 16 2013 A global existence result for the semigeostrophic equations in three dimensional convex domains. Zbl 1287.35064Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio 16 2014 Geometry of minimizers for the interaction energy with mildly repulsive potentials. Zbl 1408.49035Carrillo, J. A.; Figalli, A.; Patacchini, F. S. 16 2017 A simple proof of the Morse-Sard theorem in Sobolev spaces. Zbl 1157.58002Figalli, Alessio 16 2008 Free boundary regularity in the parabolic fractional obstacle problem. Zbl 1420.35428Barrios, Begoña; Figalli, Alessio; Ros-Oton, Xavier 14 2018 On stable solutions for boundary reactions: a De Giorgi-type result in dimension \(4 + 1\). Zbl 1441.35254Figalli, Alessio; Serra, Joaquim 14 2020 Existence, uniqueness, and regularity of optimal transport maps. Zbl 1132.28322Figalli, Alessio 14 2007 A note on Cheeger sets. Zbl 1168.39008Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo 14 2009 High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces. Zbl 1114.37034Abbondandolo, Alberto; Figalli, Alessio 14 2007 Regularity theory for local and nonlocal minimal surfaces: an overview. Zbl 1385.49028Cozzi, Matteo; Figalli, Alessio 14 2017 Stable solutions to semilinear elliptic equations are smooth up to dimension \(9\). Zbl 1467.35172Cabré, Xavier; Figalli, Alessio; Ros-Oton, Xavier; Serra, Joaquim 13 2020 Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces. Zbl 1228.60063Ambrosio, Luigi; Figalli, Alessio 12 2011 Absolute continuity of Wasserstein geodesics in the Heisenberg group. Zbl 1246.53049Figalli, A.; Juillet, N. 12 2008 Universality in several-matrix models via approximate transport maps. Zbl 1402.60009Figalli, Alessio; Guionnet, Alice 11 2016 Second order stability for the Monge-Ampère equation and strong Sobolev convergence of optimal transport maps. Zbl 1278.35090De Philippis, Guido; Figalli, Alessio 11 2013 On the Lagrangian structure of transport equations: the Vlasov-Poisson system. Zbl 1403.35085Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio 11 2017 Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow. Zbl 1384.35130Figalli, Alessio; Kang, Moon-Jin; Morales, Javier 11 2018 Quantitative stability for sumsets in \(\mathbb R^n\). Zbl 1325.49052Figalli, Alessio; Jerison, David 10 2015 Local semiconvexity of Kantorovich potentials on non-compact manifolds. Zbl 1228.49047Figalli, Alessio; Gigli, Nicola 10 2011 On flows of \(H ^{3/2}\)-vector fields on the circle. Zbl 1195.46032Figalli, Alessio 10 2010 Regularity results for very degenerate elliptic equations. Zbl 1282.35175Colombo, Maria; Figalli, Alessio 10 2014 Regularity of optimal transport maps (after Ma-Trudinger-Wang and Loeper). Zbl 1211.49054Figalli, Alessio 9 2010 Optimal regularity of the convex envelope. Zbl 1316.49019De Philippis, Guido; Figalli, Alessio 9 2015 Symmetry results for critical anisotropic \(p\)-Laplacian equations in convex cones. Zbl 1453.35104Ciraolo, Giulio; Figalli, Alessio; Roncoroni, Alberto 9 2020 Generic regularity of free boundaries for the obstacle problem. Zbl 1456.35234Figalli, Alessio; Ros-Oton, Xavier; Serra, Joaquim 8 2020 Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations. Zbl 1392.35144Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis 8 2018 Generalized solutions for the Euler equations in one and two dimensions. Zbl 1170.35078Bernot, Marc; Figalli, Alessio; Santambrogio, Filippo 8 2009 Convergence to the viscous porous medium equation and propagation of chaos. Zbl 1180.35592Figalli, Alessio; Philipowski, Robert 7 2008 Rigidity and stability of Caffarelli’s log-concave perturbation theorem. Zbl 1359.60050De Philippis, Guido; Figalli, Alessio 7 2017 Gradient stability for the Sobolev inequality: the case \(p\geq 2\). Zbl 1417.46023Figalli, Alessio; Neumayer, Robin 7 2019 Semiclassical limit for mixed states with singular and rough potentials. Zbl 1264.81177Figalli, Alessio; Ligabò, Marilena; Paul, Thierry 7 2012 An approximation lemma about the cut locus, with applications in optimal transport theory. Zbl 1172.53022Figalli, Alessio; Villani, Cédric 7 2008 Regularity of monotone transport maps between unbounded domains. Zbl 1448.35188Cordero-Erausquin, Dario; Figalli, Alessio 7 2019 On the regularity of the free boundary in the \(p\)-Laplacian obstacle problem. Zbl 1387.35631Figalli, Alessio; Krummel, Brian; Ros-Oton, Xavier 7 2017 On the continuity of center-outward distribution and quantile functions. Zbl 1433.62132Figalli, Alessio 6 2018 A note on the regularity of the free boundaries in the optimal partial transport problem. Zbl 1183.35277Figalli, Alessio 6 2009 Almost everywhere well-posedness of continuity equations with measure initial data. (Existence presque partout des équations de continuité avec données initiales mesures.) Zbl 1195.35202Ambrosio, Luigi; Figalli, Alessio 6 2010 Boundary \(\varepsilon\)-regularity in optimal transportation. Zbl 1307.49045Chen, Shibing; Figalli, Alessio 6 2015 Synchronized traffic plans and stability of optima. Zbl 1148.49039Bernot, Marc; Figalli, Alessio 6 2008 An overview of unconstrained free boundary problems. Zbl 1353.35322Figalli, Alessio; Shahgholian, Henrik 6 2015 Closing Aubry sets. II. Zbl 1377.37090Figalli, A.; Rifford, L. 6 2015 A general class of free boundary problems for fully nonlinear parabolic equations. Zbl 1338.35508Figalli, Alessio; Shahgholian, Henrik 6 2015 A variational method for a class of parabolic PDEs. Zbl 1239.35074Figalli, Alessio; Gangbo, Wilfrid; Yolcu, Turkay 5 2011 On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces. Zbl 1282.28002Ambrosio, Luigi; Figalli, Alessio; Runa, Eris 5 2013 Sobolev regularity for Monge-Ampère type equations. Zbl 1271.49031De Philippis, Guido; Figalli, Alessio 5 2013 Strong stability for the Wulff inequality with a crystalline norm. Zbl 07492702Figalli, Alessio; Zhang, Yi Ru-Ya 1 2022 Sharp extinction rates for fast diffusion equations on generic bounded domains. Zbl 1467.35047Bonforte, Matteo; Figalli, Alessio 1 2021 An invitation to optimal transport, Wasserstein distances, and gradient flows. Zbl 1472.49001Figalli, Alessio; Glaudo, Federico 1 2021 On stable solutions for boundary reactions: a De Giorgi-type result in dimension \(4 + 1\). Zbl 1441.35254Figalli, Alessio; Serra, Joaquim 14 2020 Stable solutions to semilinear elliptic equations are smooth up to dimension \(9\). Zbl 1467.35172Cabré, Xavier; Figalli, Alessio; Ros-Oton, Xavier; Serra, Joaquim 13 2020 Symmetry results for critical anisotropic \(p\)-Laplacian equations in convex cones. Zbl 1453.35104Ciraolo, Giulio; Figalli, Alessio; Roncoroni, Alberto 9 2020 Generic regularity of free boundaries for the obstacle problem. Zbl 1456.35234Figalli, Alessio; Ros-Oton, Xavier; Serra, Joaquim 8 2020 On the sharp stability of critical points of the Sobolev inequality. Zbl 1440.35163Figalli, Alessio; Glaudo, Federico 2 2020 Optimal regularity and structure of the free boundary for minimizers in cohesive zone models. Zbl 1442.49005Caffarelli, L.; Cagnetti, F.; Figalli, A. 2 2020 A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment. Zbl 1405.35206Figalli, Alessio; Kang, Moon-Jin 29 2019 On the fine structure of the free boundary for the classical obstacle problem. Zbl 1408.35228Figalli, Alessio; Serra, Joaquim 16 2019 Gradient stability for the Sobolev inequality: the case \(p\geq 2\). Zbl 1417.46023Figalli, Alessio; Neumayer, Robin 7 2019 Regularity of monotone transport maps between unbounded domains. Zbl 1448.35188Cordero-Erausquin, Dario; Figalli, Alessio 7 2019 Optimal regularity for the convex envelope and semiconvex functions related to supersolutions of fully nonlinear elliptic equations. Zbl 07046610Braga, J. Ederson M.; Figalli, Alessio; Moreira, Diego 4 2019 Global regularity for the free boundary in the obstacle problem for the fractional Laplacian. Zbl 1409.35044Barrios, Begoña; Figalli, Alessio; Ros-Oton, Xavier 21 2018 Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains. Zbl 1443.35067Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis 21 2018 Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature. Zbl 1411.53030Ciraolo, Giulio; Figalli, Alessio; Maggi, Francesco; Novaga, Matteo 17 2018 Free boundary regularity in the parabolic fractional obstacle problem. Zbl 1420.35428Barrios, Begoña; Figalli, Alessio; Ros-Oton, Xavier 14 2018 Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow. Zbl 1384.35130Figalli, Alessio; Kang, Moon-Jin; Morales, Javier 11 2018 Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations. Zbl 1392.35144Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis 8 2018 On the continuity of center-outward distribution and quantile functions. Zbl 1433.62132Figalli, Alessio 6 2018 A quantitative analysis of metrics on \(\mathbb R^n\) with almost constant positive scalar curvature, with applications to fast diffusion flows. Zbl 1408.53018Ciraolo, Giulio; Figalli, Alessio; Maggi, Francesco 4 2018 The sharp quantitative Euclidean concentration inequality. Zbl 1385.39005Figalli, Alessio; Maggi, Francesco; Mooney, Connor 4 2018 Symplectic \(G\)-capacities and integrable systems. Zbl 1395.57034Figalli, Alessio; Palmer, Joseph; Pelayo, Álvaro 4 2018 Global existence for the semigeostrophic equations via Sobolev estimates for Monge-Ampère. Zbl 1406.35273Figalli, Alessio 2 2018 The Monge-Ampère equation and its applications. Zbl 1435.35003Figalli, Alessio 60 2017 Regularity and Bernstein-type results for nonlocal minimal surfaces. Zbl 1380.49060Figalli, Alessio; Valdinoci, Enrico 27 2017 Quantitative stability for the Brunn-Minkowski inequality. Zbl 1380.52010Figalli, Alessio; Jerison, David 21 2017 Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains. Zbl 1377.35259Bonforte, Matteo; Figalli, Alessio; Ros-Oton, Xavier 18 2017 Geometry of minimizers for the interaction energy with mildly repulsive potentials. Zbl 1408.49035Carrillo, J. A.; Figalli, A.; Patacchini, F. S. 16 2017 Regularity theory for local and nonlocal minimal surfaces: an overview. Zbl 1385.49028Cozzi, Matteo; Figalli, Alessio 14 2017 On the Lagrangian structure of transport equations: the Vlasov-Poisson system. Zbl 1403.35085Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio 11 2017 Rigidity and stability of Caffarelli’s log-concave perturbation theorem. Zbl 1359.60050De Philippis, Guido; Figalli, Alessio 7 2017 On the regularity of the free boundary in the \(p\)-Laplacian obstacle problem. Zbl 1387.35631Figalli, Alessio; Krummel, Brian; Ros-Oton, Xavier 7 2017 Characterization of isoperimetric sets inside almost-convex cones. Zbl 1355.49035Figalli, Alessio; Baer, Eric 5 2017 Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume. Zbl 1369.49065Figalli, Alessio; Jerison, David 4 2017 Lipschitz changes of variables between perturbations of log-concave measures. Zbl 1383.60006Colombo, Maria; Figalli, Alessio; Jhaveri, Yash 3 2017 Partial \(W^{2,p}\) regularity for optimal transport maps. Zbl 1364.35058Chen, Shibing; Figalli, Alessio 3 2017 Regularity of codimension-1 minimizing currents under minimal assumptions on the integrand. Zbl 1386.49060Figalli, Alessio 1 2017 BMO-type norms related to the perimeter of sets. Zbl 1352.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio 17 2016 Universality in several-matrix models via approximate transport maps. Zbl 1402.60009Figalli, Alessio; Guionnet, Alice 11 2016 On the density function on moduli spaces of toric 4-manifolds. Zbl 1386.53103Figalli, Alessio; Pelayo, Álvaro 3 2016 Nonlinear bounds in Hölder spaces for the Monge-Ampère equation. Zbl 1338.35196Figalli, Alessio; Jhaveri, Yash; Mooney, Connor 2 2016 Weak KAM theory for a weakly coupled system of Hamilton-Jacobi equations. Zbl 1355.49023Figalli, Alessio; Gomes, Diogo; Marcon, Diego 2 2016 Stability results on the smoothness of optimal transport maps with general costs. Zbl 1406.35120Chen, Shibing; Figalli, Alessio 1 2016 Isoperimetry and stability properties of balls with respect to nonlocal energies. Zbl 1312.49051Figalli, A.; Fusco, N.; Maggi, F.; Millot, V.; Morini, M. 73 2015 Transport maps for \(\beta\)-matrix models and universality. Zbl 1330.49046Bekerman, F.; Figalli, A.; Guionnet, A. 30 2015 Partial regularity for optimal transport maps. Zbl 1325.49051De Philippis, Guido; Figalli, Alessio 18 2015 Existence and uniqueness of maximal regular flows for non-smooth vector fields. Zbl 1348.34039Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio 17 2015 Quantitative stability for sumsets in \(\mathbb R^n\). Zbl 1325.49052Figalli, Alessio; Jerison, David 10 2015 Optimal regularity of the convex envelope. Zbl 1316.49019De Philippis, Guido; Figalli, Alessio 9 2015 Boundary \(\varepsilon\)-regularity in optimal transportation. Zbl 1307.49045Chen, Shibing; Figalli, Alessio 6 2015 An overview of unconstrained free boundary problems. Zbl 1353.35322Figalli, Alessio; Shahgholian, Henrik 6 2015 Closing Aubry sets. II. Zbl 1377.37090Figalli, A.; Rifford, L. 6 2015 A general class of free boundary problems for fully nonlinear parabolic equations. Zbl 1338.35508Figalli, Alessio; Shahgholian, Henrik 6 2015 Closing Aubry sets. I. Zbl 1321.37061Figalli, A.; Rifford, L. 4 2015 A note on the dimension of the singular set in free interface problems. Zbl 1340.49044De Philippis, Guido; Figalli, Alessio 4 2015 Generic hyperbolicity of aubry sets on surfaces. Zbl 1352.37169Contreras, G.; Figalli, A.; Rifford, L. 4 2015 Stability results for the Brunn-Minkowski inequality. Zbl 1346.49068Figalli, Alessio 3 2015 Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces. Zbl 1316.35061Barrios, Begoña; Figalli, Alessio; Valdinoci, Enrico 50 2014 The Monge-Ampère equation and its link to optimal transportation. Zbl 06377770De Philippis, Guido; Figalli, Alessio 47 2014 Strongly nonlocal dislocation dynamics in crystals. Zbl 1304.35731Dipierro, Serena; Figalli, Alessio; Valdinoci, Enrico 28 2014 A general class of free boundary problems for fully nonlinear elliptic equations. Zbl 1326.35137Figalli, Alessio; Shahgholian, Henrik 21 2014 A global existence result for the semigeostrophic equations in three dimensional convex domains. Zbl 1287.35064Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio 16 2014 Regularity results for very degenerate elliptic equations. Zbl 1282.35175Colombo, Maria; Figalli, Alessio 10 2014 Perimeter of sets and BMO-type norms. (Périmètre d’ensembles et normes de type BMO.) Zbl 1316.46026Ambrosio, Luigi; Bourgain, Jean; Brezis, Haïm; Figalli, Alessio 5 2014 How to recognize convexity of a set from its marginals. Zbl 1294.26022Figalli, Alessio; Jerison, David 4 2014 Higher integrability for minimizers of the Mumford-Shah functional. Zbl 1316.49044De Philippis, Guido; Figalli, Alessio 3 2014 Quantitative stability results for the Brunn-Minkowski inequality. Zbl 1373.49054Figalli, Alessio 3 2014 WKB analysis of Bohmian dynamics. Zbl 1341.35139Figalli, A.; Klein, C.; Markowich, P.; Sparber, C. 3 2014 An excess-decay result for a class of degenerate elliptic equations. Zbl 1286.35114Colombo, Maria; Figalli, Alessio 1 2014 A geometric approach to correlation inequalities in the plane. Zbl 1288.60024Figalli, A.; Maggi, F.; Pratelli, A. 1 2014 Partial regularity results in optimal transportation. Zbl 1323.49023de Philippis, G.; Figalli, A. 1 2014 Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088Caffarelli, Luis; Figalli, Alessio 51 2013 Stability for a GNS inequality and the log-HLS inequality, with application to the critical mass Keller-Segel equation. Zbl 1307.26027Carlen, Eric A.; Figalli, Alessio 35 2013 \(W^{2,1}\) regularity for solutions of the Monge-Ampère equation. Zbl 1286.35107De Philippis, Guido; Figalli, Alessio 33 2013 Asymptotics of the \(s\)-perimeter as \(s \searrow 0\). Zbl 1275.49083Dipierro, Serena; Figalli, Alessio; Palatucci, Giampiero; Valdinoci, Enrico 33 2013 A sharp stability result for the relative isoperimetric inequality inside convex cones. Zbl 1262.49045Figalli, A.; Indrei, E. 25 2013 Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation. Zbl 1286.46035Figalli, Alessio; Maggi, Francesco; Pratelli, Aldo 24 2013 A note on interior \(W^{2,1+ \varepsilon }\) estimates for the Monge-Ampère equation. Zbl 1280.35153De Philippis, G.; Figalli, A.; Savin, O. 22 2013 Hölder continuity and injectivity of optimal maps. Zbl 1281.49037Figalli, Alessio; Kim, Young-Heon; McCann, Robert J. 22 2013 Regularity of optimal transport maps on multiple products of spheres. Zbl 1268.49053Figalli, Alessio; Kim, Young-Heon; McCann, Robert J. 18 2013 On the isoperimetric problem for radial log-convex densities. Zbl 1307.49046Figalli, A.; Maggi, F. 16 2013 Second order stability for the Monge-Ampère equation and strong Sobolev convergence of optimal transport maps. Zbl 1278.35090De Philippis, Guido; Figalli, Alessio 11 2013 On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces. Zbl 1282.28002Ambrosio, Luigi; Figalli, Alessio; Runa, Eris 5 2013 Sobolev regularity for Monge-Ampère type equations. Zbl 1271.49031De Philippis, Guido; Figalli, Alessio 5 2013 On supporting hyperplanes to convex bodies. Zbl 1288.52001Figalli, Alessio; Kim, Young-Heon; McCann, Robert J. 4 2013 Aubry sets, Hamilton-Jacobi equations, and the Mañé conjecture. Zbl 1364.37137Figalli, A.; Rifford, L. 2 2013 Stability in geometric and functional inequalities. Zbl 1364.49059Figalli, Alessio 2 2013 Non-local gradient dependent operators. Zbl 1252.35099Bjorland, C.; Caffarelli, L.; Figalli, A. 54 2012 Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio 53 2012 Nearly round spheres look convex. Zbl 1241.53031Figalli, Alessio; Rifford, Ludovic; Villani, Cedric 27 2012 Existence of Eulerian solutions to the semigeostrophic equations in physical space: The 2-dimensional periodic case. Zbl 1258.35164Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio 21 2012 Confinement in nonlocal interaction equations. Zbl 1233.35032Carrillo, J. A.; Di Francesco, M.; Figalli, A.; Laurent, T.; Slepčev, D. 19 2012 Total variation flow and sign fast diffusion in one dimension. Zbl 1242.35049Bonforte, Matteo; Figalli, Alessio 17 2012 Semiclassical limit for mixed states with singular and rough potentials. Zbl 1264.81177Figalli, Alessio; Ligabò, Marilena; Paul, Thierry 7 2012 Isoperimetric-type inequalities on constant curvature manifolds. Zbl 1250.58008Figalli, Alessio; Ge, Yuxin 3 2012 Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations. Zbl 1215.35045Carrillo, J. A.; Difrancesco, M.; Figalli, A.; Laurent, T.; Slepčev, D. 119 2011 On the shape of liquid drops and crystals in the small mass regime. Zbl 1279.76005Figalli, A.; Maggi, F. 28 2011 Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data. Zbl 1231.35186Ambrosio, Luigi; Figalli, Alessio; Friesecke, Gero; Giannoulis, Johannes; Paul, Thierry 24 2011 ...and 46 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,644 Authors 82 Figalli, Alessio 46 Valdinoci, Enrico 39 Carrillo de la Plata, José Antonio 27 Dipierro, Serena 23 Novaga, Matteo 23 Röckner, Michael 20 Ambrosio, Luigi 19 Santambrogio, Filippo 17 Ros-Oton, Xavier 16 Fusco, Nicola 16 Rifford, Ludovic 15 Savin, Ovidiu V. 15 Shaposhnikov, Stanislav V. 14 Bogachev, Vladimir Igorevich 14 Maggi, Francesco 13 Vazquez, Juan Luis 12 Choi, Young-Pil 12 Ciraolo, Giulio 12 Luo, Dejun 12 Vauchelet, Nicolas 11 Brasco, Lorenzo 11 Caffarelli, Luis Ángel 11 Carlier, Guillaume 11 Indrei, Emanuel 11 McCann, Robert J. 11 Pratelli, Aldo 10 Gigli, Nicola 10 Goldman, Michael 10 Maldonado, Diego 10 Serra Montolí, Joaquim 10 Wang, Xu-Jia 9 Cabré, Xavier 9 Colombo, Maria 9 De Philippis, Guido 9 Fetecau, Razvan C. 9 Le, Nam Q. 9 Neumayer, Robin 8 Barrios Barrera, Begoña 8 Chen, Shibing 8 Cinti, Eleonora 8 Flandoli, Franco 8 Kitagawa, Jun 8 Rossi, Julio Daniel 8 Sire, Yannick 8 Topaloglu, Ihsan 8 Trevisan, Dario 7 Böröczky, Karoly jun. 7 Cesaroni, Annalisa 7 Cozzi, Matteo 7 Da Prato, Giuseppe 7 del Barrio, Eustasio 7 Fall, Mouhamed Moustapha 7 Fathi, Max 7 Jabin, Pierre-Emmanuel 7 Kim, Young-Heon 7 Lee, Paul W. Y. 7 Ohta, Shin-ichi 7 Patacchini, Francesco Saverio 7 Paul, Thierry 7 Ruffini, Berardo 7 Salani, Paolo 7 Shahgholian, Henrik 7 Velichkov, Bozhidar 7 Villani, Cédric 7 Warma, Mahamadi 7 Zhang, Xicheng 6 Abdellaoui, Boumediene 6 Bonforte, Matteo 6 Crippa, Gianluca 6 Guillen, Nestor 6 James, François 6 Lee, Ki-Ahm 6 Liu, Jiakun 6 Medina, Maria 6 Palatucci, Giampiero 6 Park, Jinwan 6 Pass, Brendan W. 6 Patrizi, Stefania 6 Peral Alonso, Ireneo 6 Slepčev, Dejan 6 Spolaor, Luca 5 Balogh, Zoltán M. 5 Bertozzi, Andrea Louise 5 Brézis, Haïm 5 Bucur, Claudia 5 Carlen, Eric Anders 5 Choksi, Rustum 5 Cicalese, Marco 5 Craig, Katy 5 da Silva, João Vítor 5 Del Pino, Manuel A. 5 del Teso, Félix 5 Erdős, László 5 Fang, Shizan 5 Fernández-Real, Xavier 5 Frank, Rupert L. 5 Gallouët, Thomas O. 5 Garofalo, Nicola 5 Guionnet, Alice 5 Julin, Vesa ...and 1,544 more Authors all top 5 Cited in 264 Serials 113 Calculus of Variations and Partial Differential Equations 65 Archive for Rational Mechanics and Analysis 63 Nonlinear Analysis. 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Matematica e Applicazioni 10 Communications in Contemporary Mathematics 10 Advances in Calculus of Variations 9 Geometric and Functional Analysis. GAFA 9 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 9 Science China. Mathematics 8 Journal für die Reine und Angewandte Mathematik 8 Interfaces and Free Boundaries 8 Bulletin of Mathematical Sciences 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Numerische Mathematik 7 SIAM Journal on Control and Optimization 7 SIAM Journal on Numerical Analysis 7 Acta Applicandae Mathematicae 7 Applied Mathematics Letters 7 Journal of Nonlinear Science 7 Discrete and Continuous Dynamical Systems. Series S 7 Séminaire Laurent Schwartz. 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Series B 4 Bollettino dell’Unione Matematica Italiana 3 Journal of Computational Physics 3 Journal of Geometry and Physics 3 The Annals of Statistics 3 Geometriae Dedicata 3 Journal of the Korean Mathematical Society 3 Journal of Optimization Theory and Applications 3 Journal of Theoretical Probability 3 Publicacions Matemàtiques 3 European Journal of Applied Mathematics 3 The Annals of Applied Probability 3 Journal of Mathematical Imaging and Vision 3 St. Petersburg Mathematical Journal 3 Journal of Convex Analysis ...and 164 more Serials all top 5 Cited in 49 Fields 916 Partial differential equations (35-XX) 442 Calculus of variations and optimal control; optimization (49-XX) 210 Probability theory and stochastic processes (60-XX) 173 Differential geometry (53-XX) 111 Functional analysis (46-XX) 110 Statistical mechanics, structure of matter (82-XX) 107 Real functions (26-XX) 100 Global analysis, analysis on manifolds (58-XX) 91 Numerical analysis (65-XX) 87 Fluid mechanics (76-XX) 83 Operator theory (47-XX) 77 Measure and integration (28-XX) 76 Biology and other natural sciences (92-XX) 70 Dynamical systems and ergodic theory (37-XX) 64 Convex and discrete geometry (52-XX) 42 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 39 Operations research, mathematical programming (90-XX) 37 Mechanics of particles and systems (70-XX) 35 Ordinary differential equations (34-XX) 35 Quantum theory (81-XX) 34 Mechanics of deformable solids (74-XX) 29 Integral equations (45-XX) 23 Statistics (62-XX) 22 Linear and multilinear algebra; matrix theory (15-XX) 21 Potential theory (31-XX) 19 Systems theory; control (93-XX) 18 Harmonic analysis on Euclidean spaces (42-XX) 15 Functions of a complex variable (30-XX) 13 Information and communication theory, circuits (94-XX) 12 Several complex variables and analytic spaces (32-XX) 12 Difference and functional equations (39-XX) 12 Computer science (68-XX) 12 Geophysics (86-XX) 8 Geometry (51-XX) 8 General topology (54-XX) 7 Combinatorics (05-XX) 7 Optics, electromagnetic theory (78-XX) 6 History and biography (01-XX) 5 General and overarching topics; collections (00-XX) 4 Topological groups, Lie groups (22-XX) 4 Approximations and expansions (41-XX) 4 Manifolds and cell complexes (57-XX) 3 Algebraic geometry (14-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Abstract harmonic analysis (43-XX) 1 Algebraic topology (55-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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