Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio On the Lagrangian structure of transport equations: the Vlasov-Poisson system. (English) Zbl 1403.35085 Duke Math. J. 166, No. 18, 3505-3568 (2017). MSC: 35F25 35Q83 34A12 37C10 35R09 PDFBibTeX XMLCite \textit{L. Ambrosio} et al., Duke Math. J. 166, No. 18, 3505--3568 (2017; Zbl 1403.35085) Full Text: DOI arXiv Euclid
Ambrosio, Luigi; Bourgain, Jean; Brezis, Haim; Figalli, Alessio BMO-type norms related to the perimeter of sets. (English) Zbl 1352.46026 Commun. Pure Appl. Math. 69, No. 6, 1062-1086 (2016). Reviewer: Thomas Zürcher (Coventry) MSC: 46E30 42B35 28A75 PDFBibTeX XMLCite \textit{L. Ambrosio} et al., Commun. Pure Appl. Math. 69, No. 6, 1062--1086 (2016; Zbl 1352.46026) Full Text: DOI arXiv
Ambrosio, Luigi; Colombo, Maria; Figalli, Alessio Existence and uniqueness of maximal regular flows for non-smooth vector fields. (English) Zbl 1348.34039 Arch. Ration. Mech. Anal. 218, No. 2, 1043-1081 (2015). Reviewer: Przemysław Górka (Warsaw) MSC: 34A36 37C60 34C11 PDFBibTeX XMLCite \textit{L. Ambrosio} et al., Arch. Ration. Mech. Anal. 218, No. 2, 1043--1081 (2015; Zbl 1348.34039) Full Text: DOI arXiv
Ambrosio, Luigi; Figalli, Alessio Lecture notes on variational models for incompressible Euler equations. (English) Zbl 1426.76624 Ollivier, Yann (ed.) et al., Optimal transport. Theory and applications. Proceedings of the summer school ‘Optimal transportation: theory and applications’, Fourier Institute, Grenoble, France. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 413, 58-71 (2014). MSC: 76M30 76B03 PDFBibTeX XMLCite \textit{L. Ambrosio} and \textit{A. Figalli}, Lond. Math. Soc. Lect. Note Ser. 413, 58--71 (2014; Zbl 1426.76624) Full Text: arXiv
Ambrosio, Luigi; Bourgain, Jean; Brezis, Haïm; Figalli, Alessio Perimeter of sets and BMO-type norms. (Périmètre d’ensembles et normes de type BMO.) (English. French summary) Zbl 1316.46026 C. R., Math., Acad. Sci. Paris 352, No. 9, 697-698 (2014). MSC: 46E30 PDFBibTeX XMLCite \textit{L. Ambrosio} et al., C. R., Math., Acad. Sci. Paris 352, No. 9, 697--698 (2014; Zbl 1316.46026) Full Text: DOI
Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio A global existence result for the semigeostrophic equations in three dimensional convex domains. (English) Zbl 1287.35064 Discrete Contin. Dyn. Syst. 34, No. 4, 1251-1268 (2014). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 35Q35 35J60 86A10 PDFBibTeX XMLCite \textit{L. Ambrosio} et al., Discrete Contin. Dyn. Syst. 34, No. 4, 1251--1268 (2014; Zbl 1287.35064) Full Text: DOI arXiv
Ambrosio, Luigi; Figalli, Alessio; Runa, Eris On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces. (English) Zbl 1282.28002 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 24, No. 1, 111-122 (2013). Reviewer: Boris A. Kats (Kazan) MSC: 28A75 26B30 28C20 60H30 PDFBibTeX XMLCite \textit{L. Ambrosio} et al., Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 24, No. 1, 111--122 (2013; Zbl 1282.28002) Full Text: DOI arXiv
Ambrosio, Luigi; Figalli, Alessio; Friesecke, Gero; Giannoulis, Johannes; Paul, Thierry Corrigendum: Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data. (English) Zbl 1258.35167 Commun. Pure Appl. Math. 66, No. 4, 646-647 (2013). MSC: 35Q40 35R05 81S30 81V55 PDFBibTeX XMLCite \textit{L. Ambrosio} et al., Commun. Pure Appl. Math. 66, No. 4, 646--647 (2013; Zbl 1258.35167) Full Text: DOI
Ambrosio, Luigi; Colombo, Maria; De Philippis, Guido; Figalli, Alessio Existence of Eulerian solutions to the semigeostrophic equations in physical space: The 2-dimensional periodic case. (English) Zbl 1258.35164 Commun. Partial Differ. Equations 37, No. 10-12, 2209-2227 (2012). MSC: 35Q35 35J60 76B03 86A10 PDFBibTeX XMLCite \textit{L. Ambrosio} et al., Commun. Partial Differ. Equations 37, No. 10--12, 2209--2227 (2012; Zbl 1258.35164) Full Text: DOI arXiv
Ambrosio, Luigi; Crippa, Gianluca; Figalli, Alessio; Spinolo, Laura V. Existence and uniqueness results for the continuity equation and applications to the chromatography system. (English) Zbl 1248.35119 Bressan, Alberto (ed.) et al., Nonlinear conservation laws and applications. Proceedings of the summer program, IMA, Minneapolis, MN, USA, July 13–31, 2009. New York, NY: Springer (ISBN 978-1-4419-9553-7; 978-1-4419-9554-4/ebook). The IMA Volumes in Mathematics and its Applications 153, 195-204 (2011). MSC: 35L65 35F10 PDFBibTeX XMLCite \textit{L. Ambrosio} et al., IMA Vol. Math. Appl. 153, 195--204 (2011; Zbl 1248.35119) Full Text: DOI
Ambrosio, Luigi; Figalli, Alessio; Friesecke, Gero; Giannoulis, Johannes; Paul, Thierry Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data. (English) Zbl 1231.35186 Commun. Pure Appl. Math. 64, No. 9, 1199-1242 (2011). Reviewer: Michael Perelmuter (Kyïv) MSC: 35Q40 35R05 81S30 81V55 PDFBibTeX XMLCite \textit{L. Ambrosio} et al., Commun. Pure Appl. Math. 64, No. 9, 1199--1242 (2011; Zbl 1231.35186) Full Text: DOI arXiv
Ambrosio, Luigi; Figalli, Alessio Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces. (English) Zbl 1228.60063 Ann. Fac. Sci. Toulouse, Math. (6) 20, No. 2, 407-438 (2011). Reviewer: Toader Morozan (Bucureşti) MSC: 60H10 PDFBibTeX XMLCite \textit{L. Ambrosio} and \textit{A. Figalli}, Ann. Fac. Sci. Toulouse, Math. (6) 20, No. 2, 407--438 (2011; Zbl 1228.60063) Full Text: DOI arXiv EuDML
Ambrosio, Luigi; Figalli, Alessio Almost everywhere well-posedness of continuity equations with measure initial data. (Existence presque partout des équations de continuité avec données initiales mesures.) (English) Zbl 1195.35202 C. R., Math., Acad. Sci. Paris 348, No. 5-6, 249-252 (2010). MSC: 35L45 35A01 35A02 35R05 PDFBibTeX XMLCite \textit{L. Ambrosio} and \textit{A. Figalli}, C. R., Math., Acad. Sci. Paris 348, No. 5--6, 249--252 (2010; Zbl 1195.35202) Full Text: DOI arXiv
Ambrosio, Luigi; Crippa, Gianluca; Figalli, Alessio; Spinolo, Laura V. Some new well-posedness results for continuity and transport equations, and applications to the chromatography system. (English) Zbl 1222.35060 SIAM J. Math. Anal. 41, No. 5, 1890-1920 (2009). Reviewer: Evgeniy Panov (Novgorod) MSC: 35F10 35L65 PDFBibTeX XMLCite \textit{L. Ambrosio} et al., SIAM J. Math. Anal. 41, No. 5, 1890--1920 (2009; Zbl 1222.35060) Full Text: DOI arXiv
Ambrosio, Luigi; Figalli, Alessio Geodesics in the space of measure-preserving maps and plans. (English) Zbl 1253.76007 Arch. Ration. Mech. Anal. 194, No. 2, 421-462 (2009). MSC: 76B03 76M30 35Q35 PDFBibTeX XMLCite \textit{L. Ambrosio} and \textit{A. Figalli}, Arch. Ration. Mech. Anal. 194, No. 2, 421--462 (2009; Zbl 1253.76007) Full Text: DOI arXiv
Ambrosio, Luigi; Figalli, Alessio On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions. (English) Zbl 1156.60036 J. Funct. Anal. 256, No. 1, 179-214 (2009). MSC: 60H10 60H07 PDFBibTeX XMLCite \textit{L. Ambrosio} and \textit{A. Figalli}, J. Funct. Anal. 256, No. 1, 179--214 (2009; Zbl 1156.60036) Full Text: DOI arXiv
Ambrosio, Luigi; Figalli, Alessio On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations. (English) Zbl 1138.49031 Calc. Var. Partial Differ. Equ. 31, No. 4, 497-509 (2008). MSC: 49N60 49J45 76B03 PDFBibTeX XMLCite \textit{L. Ambrosio} and \textit{A. Figalli}, Calc. Var. Partial Differ. Equ. 31, No. 4, 497--509 (2008; Zbl 1138.49031) Full Text: DOI