Barles, G. Local gradient estimates for second-order nonlinear elliptic and parabolic equations by the weak Bernstein’s method. (English) Zbl 1480.35069 SN Partial Differ. Equ. Appl. 2, No. 6, Paper No. 71, 15 p. (2021). MSC: 35B45 35D40 35J15 35K10 PDFBibTeX XMLCite \textit{G. Barles}, SN Partial Differ. Equ. Appl. 2, No. 6, Paper No. 71, 15 p. (2021; Zbl 1480.35069) Full Text: DOI arXiv HAL
Barles, Guy; Quaas, Alexander; Rodríguez-Paredes, Andrei Large-time behavior of unbounded solutions of viscous Hamilton-Jacobi equations in \(\mathbb{R}^N\). (English) Zbl 1467.35046 Commun. Partial Differ. Equations 46, No. 3, 547-572 (2021). MSC: 35B40 35B51 35D40 35F21 35K15 35K55 PDFBibTeX XMLCite \textit{G. Barles} et al., Commun. Partial Differ. Equations 46, No. 3, 547--572 (2021; Zbl 1467.35046) Full Text: DOI arXiv
Barles, Guy; Ley, Olivier; Nguyen, Thi-Tuyen; Phan, Thanh Viet Large time behavior of unbounded solutions of first-order Hamilton-Jacobi equations in \(\mathbb R^N\). (English) Zbl 1431.35194 Asymptotic Anal. 112, No. 1-2, 1-22 (2019). Reviewer: Dmitry Pelinovsky (Hamilton) MSC: 35Q70 35F21 35B40 70H20 35D40 35C07 PDFBibTeX XMLCite \textit{G. Barles} et al., Asymptotic Anal. 112, No. 1--2, 1--22 (2019; Zbl 1431.35194) Full Text: DOI arXiv
Barles, G.; Briani, A.; Chasseigne, E.; Imbert, C. Flux-limited and classical viscosity solutions for regional control problems. (English) Zbl 1414.49032 ESAIM, Control Optim. Calc. Var. 24, No. 4, 1881-1906 (2018). MSC: 49L20 49L25 35F21 PDFBibTeX XMLCite \textit{G. Barles} et al., ESAIM, Control Optim. Calc. Var. 24, No. 4, 1881--1906 (2018; Zbl 1414.49032) Full Text: DOI arXiv
Barles, Guy; Chasseigne, Emmanuel Corrigendum to: “(Almost) everything you always wanted to know about deterministic control problems in stratified domains”. (English) Zbl 1406.49026 Netw. Heterog. Media 13, No. 2, 373-378 (2018). MSC: 49L25 49L20 35F21 35D40 PDFBibTeX XMLCite \textit{G. Barles} and \textit{E. Chasseigne}, Netw. Heterog. Media 13, No. 2, 373--378 (2018; Zbl 1406.49026) Full Text: DOI
Barles, Guy; Ley, Olivier; Topp, Erwin Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior. (English) Zbl 1358.35221 Nonlinearity 30, No. 2, 703-734 (2017). MSC: 35R09 35B51 35B65 35D40 35B10 35B40 PDFBibTeX XMLCite \textit{G. Barles} et al., Nonlinearity 30, No. 2, 703--734 (2017; Zbl 1358.35221) Full Text: DOI arXiv
Briani, A.; Barles, G.; Chasseigne, E.; Tchou, N. A homogenization result for a periodic Hamilton-Jacobi equation on a heterogeneous lattice. (Un résultat d’homogénéisation pour une équation de Hamilton-Jacobi périodique sur un réseau hétérogène.) (French. English summary) Zbl 1378.35019 Dogbe, Christian (ed.), Actes du colloque “EDP-Normandie”, Le Havre, France, Octobre 21–22, 2015. [s.l.]: Fédération Normandie-Mathématiques (ISBN 978-2-9541221-3-7/pbk). Normandie-Mathématiques, 107-118 (2016). MSC: 35B27 35F21 35D40 PDFBibTeX XMLCite \textit{A. Briani} et al., in: Actes du colloque ``EDP-Normandie'', Le Havre, France, Octobre 21--22, 2015. [s.l.]: Fédération Normandie-Mathématiques. 107--118 (2016; Zbl 1378.35019)
Barles, Guy; Topp, Erwin Existence, uniqueness, and asymptotic behavior for nonlocal parabolic problems with dominating gradient terms. (English) Zbl 1439.35509 SIAM J. Math. Anal. 48, No. 2, 1512-1547 (2016). MSC: 35R09 35B40 35B51 35D40 35B65 PDFBibTeX XMLCite \textit{G. Barles} and \textit{E. Topp}, SIAM J. Math. Anal. 48, No. 2, 1512--1547 (2016; Zbl 1439.35509) Full Text: DOI arXiv
Barles, Guy; Chasseigne, Emmanuel On the regularizing effect for unbounded solutions of first-order Hamilton-Jacobi equations. (English) Zbl 1342.35065 J. Differ. Equations 260, No. 9, 7020-7031 (2016). MSC: 35F21 35D35 35D40 PDFBibTeX XMLCite \textit{G. Barles} and \textit{E. Chasseigne}, J. Differ. Equations 260, No. 9, 7020--7031 (2016; Zbl 1342.35065) Full Text: DOI arXiv
Barles, Guy; Topp, Erwin Lipschitz regularity for censored subdiffusive integro-differential equations with superfractional gradient terms. (English) Zbl 1335.35266 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 131, 3-31 (2016). Reviewer: Mohammed El Aïdi (Bogotá) MSC: 35R09 35B51 35B65 35D40 35B10 35B40 PDFBibTeX XMLCite \textit{G. Barles} and \textit{E. Topp}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 131, 3--31 (2016; Zbl 1335.35266) Full Text: DOI arXiv
Barles, Guy; Briani, Ariela; Chasseigne, Emmanuel; Tchou, Nicoletta Homogenization results for a deterministic multi-domains periodic control problem. (English) Zbl 1338.49005 Asymptotic Anal. 95, No. 3-4, 243-278 (2015). MSC: 49J20 35B27 49L25 PDFBibTeX XMLCite \textit{G. Barles} et al., Asymptotic Anal. 95, No. 3--4, 243--278 (2015; Zbl 1338.49005) Full Text: DOI arXiv
Chasseigne, Emmanuel; Barles, Guy (Almost) everything you always wanted to know about deterministic control problems in stratified domains. (English) Zbl 1346.49039 Netw. Heterog. Media 10, No. 4, 809-836 (2015); corrigendum ibid. 13, No. 2, 373-378 (2018). MSC: 49L25 49L20 35F21 35D40 PDFBibTeX XMLCite \textit{E. Chasseigne} and \textit{G. Barles}, Netw. Heterog. Media 10, No. 4, 809--836 (2015; Zbl 1346.49039) Full Text: DOI arXiv
Barles, Guy; Koike, Shigeaki; Ley, Olivier; Topp, Erwin Regularity results and large time behavior for integro-differential equations with coercive Hamiltonians. (English) Zbl 1336.35347 Calc. Var. Partial Differ. Equ. 54, No. 1, 539-572 (2015). Reviewer: Giuseppe Di Fazio (Catania) MSC: 35R09 35B51 35B65 35D40 35B10 35B40 PDFBibTeX XMLCite \textit{G. Barles} et al., Calc. Var. Partial Differ. Equ. 54, No. 1, 539--572 (2015; Zbl 1336.35347) Full Text: DOI arXiv
Attouchi, A.; Barles, G. Global continuation beyond singularities on the boundary for a degenerate diffusive Hamilton-Jacobi equation. (English. French summary) Zbl 1359.35091 J. Math. Pures Appl. (9) 104, No. 2, 383-402 (2015). Reviewer: Fabio Bagagiolo (Trento) MSC: 35K20 49L25 53C44 35B50 35B05 PDFBibTeX XMLCite \textit{A. Attouchi} and \textit{G. Barles}, J. Math. Pures Appl. (9) 104, No. 2, 383--402 (2015; Zbl 1359.35091) Full Text: DOI arXiv
Barles, G.; Briani, A.; Chasseigne, E. A Bellman approach for regional optimal control problems in \(\mathbb{R}^N\). (English) Zbl 1297.49041 SIAM J. Control Optim. 52, No. 3, 1712-1744 (2014). MSC: 49L20 49L25 35F21 PDFBibTeX XMLCite \textit{G. Barles} et al., SIAM J. Control Optim. 52, No. 3, 1712--1744 (2014; Zbl 1297.49041) Full Text: DOI arXiv
Barles, Guy; Chasseigne, Emmanuel; Georgelin, Christine; Jakobsen, Espen R. On Neumann type problems for nonlocal equations set in a half space. (English) Zbl 1323.35192 Trans. Am. Math. Soc. 366, No. 9, 4873-4917 (2014). Reviewer: Ioannis P. Stavroulakis (Ioannina) MSC: 35R09 45K05 35D40 PDFBibTeX XMLCite \textit{G. Barles} et al., Trans. Am. Math. Soc. 366, No. 9, 4873--4917 (2014; Zbl 1323.35192) Full Text: DOI arXiv
Barles, Guy; Chasseigne, Emmanuel; Ciomaga, Adina; Imbert, Cyril Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations. (English) Zbl 1293.35037 Calc. Var. Partial Differ. Equ. 50, No. 1-2, 283-304 (2014). MSC: 35B40 35R09 35D40 35K15 PDFBibTeX XMLCite \textit{G. Barles} et al., Calc. Var. Partial Differ. Equ. 50, No. 1--2, 283--304 (2014; Zbl 1293.35037) Full Text: DOI arXiv
Barles, Guy; Georgelin, Christine; Jakobsen, Espen R. On Neumann and oblique derivatives boundary conditions for nonlocal elliptic equations. (English) Zbl 1285.35122 J. Differ. Equations 256, No. 4, 1368-1394 (2014). MSC: 35R09 45K05 PDFBibTeX XMLCite \textit{G. Barles} et al., J. Differ. Equations 256, No. 4, 1368--1394 (2014; Zbl 1285.35122) Full Text: DOI arXiv
Taghipoor, Masoomeh; Barles, Guy; Georgelin, Christine; Licois, Jean-René; Lescoat, Philippe Mathematical homogenization in the modelling of digestion in the small intestine. (English) Zbl 1350.92011 MathS In Action 6, No. 1, 1-19 (2013). MSC: 92C30 35B27 34C29 PDFBibTeX XMLCite \textit{M. Taghipoor} et al., MathS In Action 6, No. 1, 1--19 (2013; Zbl 1350.92011) Full Text: DOI arXiv
Barles, Guy; Ishii, Hitoshi; Mitake, Hiroyoshi A new PDE approach to the large time asymptotics of solutions of Hamilton-Jacobi equations. (English) Zbl 1284.35065 Bull. Math. Sci. 3, No. 3, 363-388 (2013). MSC: 35B40 35F21 35D40 35F31 49L25 PDFBibTeX XMLCite \textit{G. Barles} et al., Bull. Math. Sci. 3, No. 3, 363--388 (2013; Zbl 1284.35065) Full Text: DOI arXiv
Barles, Guy; Mironescu, Elisabeth On homogenization problems for fully nonlinear equations with oscillating Dirichlet boundary conditions. (English) Zbl 1278.35087 Asymptotic Anal. 82, No. 3-4, 187-200 (2013). MSC: 35J60 35D40 35B40 35K61 35B27 PDFBibTeX XMLCite \textit{G. Barles} and \textit{E. Mironescu}, Asymptotic Anal. 82, No. 3--4, 187--200 (2013; Zbl 1278.35087) Full Text: DOI arXiv
Barles, G.; Briani, A.; Chasseigne, E. A Bellman approach for two-domains optimal control problems in \(\mathbb{R}^N\). (English) Zbl 1287.49028 ESAIM, Control Optim. Calc. Var. 19, No. 3, 710-739 (2013). Reviewer: Fabio Bagagiolo (Trento) MSC: 49L25 49L20 35F21 PDFBibTeX XMLCite \textit{G. Barles} et al., ESAIM, Control Optim. Calc. Var. 19, No. 3, 710--739 (2013; Zbl 1287.49028) Full Text: DOI arXiv
Barles, Guy An introduction to the theory of viscosity solutions for first-order Hamilton-Jacobi equations and applications. (English) Zbl 1269.49043 Loreti, Paola (ed.) et al., Hamilton-Jacobi equations: approximations, numerical analysis and applications. Based on the lectures of the CIME summer school, Cetraro, Italy, August 29–September 3, 2011. Berlin: Springer; Florence: Fondazione CIME (ISBN 978-3-642-36432-7/pbk; 978-3-642-36433-4/ebook). Lecture Notes in Mathematics 2074. CIME Foundation Subseries, 49-109 (2013). MSC: 49L25 PDFBibTeX XMLCite \textit{G. Barles}, Lect. Notes Math. 2074, 49--109 (2013; Zbl 1269.49043) Full Text: DOI
Mirrahimi, Sepideh; Barles, Guy; Perthame, Benoît; Souganidis, Panagiotis E. A singular Hamilton-Jacobi equation modeling the tail problem. (English) Zbl 1280.35007 SIAM J. Math. Anal. 44, No. 6, 4297-4319 (2012). Reviewer: Georgii Sviridyuk (Chelyabinsk) MSC: 35B25 35K57 49L25 92D15 35F21 35B40 PDFBibTeX XMLCite \textit{S. Mirrahimi} et al., SIAM J. Math. Anal. 44, No. 6, 4297--4319 (2012; Zbl 1280.35007) Full Text: DOI arXiv
Barles, Guy; Ishii, Hitoshi; Mitake, Hiroyoshi On the large time behavior of solutions of Hamilton-Jacobi equations associated with nonlinear boundary conditions. (English) Zbl 1282.70037 Arch. Ration. Mech. Anal. 204, No. 2, 515-558 (2012). MSC: 70H20 35Q70 49L25 PDFBibTeX XMLCite \textit{G. Barles} et al., Arch. Ration. Mech. Anal. 204, No. 2, 515--558 (2012; Zbl 1282.70037) Full Text: DOI arXiv
Barles, Guy; Chasseigne, Emmanuel; Ciomaga, Adina; Imbert, Cyril Lipschitz regularity of solutions for mixed integro-differential equations. (English) Zbl 1298.35033 J. Differ. Equations 252, No. 11, 6012-6060 (2012). Reviewer: Vincenzo Vespri (Firenze) MSC: 35D40 35B65 35J60 35R09 PDFBibTeX XMLCite \textit{G. Barles} et al., J. Differ. Equations 252, No. 11, 6012--6060 (2012; Zbl 1298.35033) Full Text: DOI arXiv
Barles, Guy; Mitake, Hiroyoshi A PDE approach to large-time asymptotics for boundary-value problems for nonconvex Hamilton-Jacobi equations. (English) Zbl 1243.35021 Commun. Partial Differ. Equations 37, No. 1-3, 136-168 (2012). Reviewer: Sergiu Aizicovici (Athens/Ohio) MSC: 35B40 35F30 35F21 35D40 PDFBibTeX XMLCite \textit{G. Barles} and \textit{H. Mitake}, Commun. Partial Differ. Equations 37, No. 1--3, 136--168 (2012; Zbl 1243.35021) Full Text: DOI arXiv
Barles, Guy; Ley, Olivier; Mitake, Hiroyoshi Short time uniqueness results for solutions of nonlocal and non-monotone geometric equations. (English) Zbl 1246.35013 Math. Ann. 352, No. 2, 409-451 (2012). Reviewer: Shu-Yu Hsu (Min-hsiung) MSC: 35A02 35K15 49L25 45K05 53C44 35D40 35R09 PDFBibTeX XMLCite \textit{G. Barles} et al., Math. Ann. 352, No. 2, 409--451 (2012; Zbl 1246.35013) Full Text: DOI arXiv
Barles, Guy; Cesaroni, Annalisa; Novaga, Matteo Homogenization of fronts in highly heterogeneous media. (English) Zbl 1228.35026 SIAM J. Math. Anal. 43, No. 1, 212-227 (2011). Reviewer: Adrian Muntean (Eindhoven) MSC: 35B27 53C44 49L25 35D40 35K59 PDFBibTeX XMLCite \textit{G. Barles} et al., SIAM J. Math. Anal. 43, No. 1, 212--227 (2011; Zbl 1228.35026) Full Text: DOI HAL
Barles, Guy; Chasseigne, Emmanuel; Imbert, Cyril Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations. (English) Zbl 1207.35277 J. Eur. Math. Soc. (JEMS) 13, No. 1, 1-26 (2011). Reviewer: Rodica Luca Tudorache (Iaşi) MSC: 35R09 35D40 35J60 35B05 45K05 47G20 PDFBibTeX XMLCite \textit{G. Barles} et al., J. Eur. Math. Soc. (JEMS) 13, No. 1, 1--26 (2011; Zbl 1207.35277) Full Text: DOI arXiv
Barles, Guy; Porretta, Alessio; Tchamba, Thierry Tabet On the large time behavior of solutions of the Dirichlet problem for subquadratic viscous Hamilton-Jacobi equations. (English) Zbl 1209.37069 J. Math. Pures Appl. (9) 94, No. 5, 497-519 (2010). Reviewer: George Stoica (Saint John) MSC: 37K05 35F21 70H20 PDFBibTeX XMLCite \textit{G. Barles} et al., J. Math. Pures Appl. (9) 94, No. 5, 497--519 (2010; Zbl 1209.37069) Full Text: DOI arXiv
El Farouq, Naïma; Barles, Guy; Bernhard, Pierre Deterministic minimax impulse control. (English) Zbl 1198.49025 Appl. Math. Optim. 61, No. 3, 353-378 (2010). MSC: 49L25 49N25 49N70 49J40 PDFBibTeX XMLCite \textit{N. El Farouq} et al., Appl. Math. Optim. 61, No. 3, 353--378 (2010; Zbl 1198.49025) Full Text: DOI
Barles, Guy; Laurençot, Philippe; Stinner, Christian Convergence to steady states for radially symmetric solutions to a quasilinear degenerate diffusive Hamilton-Jacobi equation. (English) Zbl 1211.35042 Asymptotic Anal. 67, No. 3-4, 229-250 (2010). MSC: 35B40 35K92 35K20 35F21 35D40 35K65 PDFBibTeX XMLCite \textit{G. Barles} et al., Asymptotic Anal. 67, No. 3--4, 229--250 (2010; Zbl 1211.35042) Full Text: DOI arXiv
Barles, Guy A short proof of the \(C^{0,\alpha }\)-regularity of viscosity subsolutions for superquadratic viscous Hamilton-Jacobi equations and applications. (English) Zbl 1190.35081 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 1, 31-47 (2010). MSC: 35J60 35B65 35J65 35J70 49L25 PDFBibTeX XMLCite \textit{G. Barles}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 1, 31--47 (2010; Zbl 1190.35081) Full Text: DOI arXiv
Barles, Guy; Dharmatti, Sheetal; Ramaswamy, Mythily Unbounded viscosity solutions of hybrid control systems. (English) Zbl 1183.49026 ESAIM, Control Optim. Calc. Var. 16, No. 1, 176-193 (2010). MSC: 49L20 49L25 93C30 93C15 93C10 PDFBibTeX XMLCite \textit{G. Barles} et al., ESAIM, Control Optim. Calc. Var. 16, No. 1, 176--193 (2010; Zbl 1183.49026) Full Text: DOI arXiv EuDML
Barles, Guy; Mirrahimi, Sepideh; Perthame, Benoît Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result. (English) Zbl 1204.35027 Methods Appl. Anal. 16, No. 3, 321-340 (2009). MSC: 35B25 35K57 47G20 49L25 92D15 35F21 PDFBibTeX XMLCite \textit{G. Barles} et al., Methods Appl. Anal. 16, No. 3, 321--340 (2009; Zbl 1204.35027) Full Text: DOI arXiv Euclid
Barles, Guy; Cardaliaguet, Pierre; Ley, Olivier; Monteillet, Aurélien Uniqueness results for nonlocal Hamilton-Jacobi equations. (English) Zbl 1169.49028 J. Funct. Anal. 257, No. 5, 1261-1287 (2009). MSC: 49L25 35F25 35Q72 PDFBibTeX XMLCite \textit{G. Barles} et al., J. Funct. Anal. 257, No. 5, 1261--1287 (2009; Zbl 1169.49028) Full Text: DOI arXiv
Barles, Guy; Cardaliaguet, Pierre; Ley, Olivier; Monteillet, Aurélien Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations. (English) Zbl 1166.49027 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7-8, 2801-2810 (2009). MSC: 49L25 35F25 35K65 35A05 35D05 45G10 47H10 PDFBibTeX XMLCite \textit{G. Barles} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7--8, 2801--2810 (2009; Zbl 1166.49027) Full Text: DOI arXiv
Perthame, Benoit; Barles, Guy Dirac concentrations in Lotka-Volterra parabolic PDEs. (English) Zbl 1172.35005 Indiana Univ. Math. J. 57, No. 7, 3275-3302 (2008). Reviewer: Denise Huet (Nancy) MSC: 35B25 35K57 49L25 92D15 45K05 35B40 92D25 PDFBibTeX XMLCite \textit{B. Perthame} and \textit{G. Barles}, Indiana Univ. Math. J. 57, No. 7, 3275--3302 (2008; Zbl 1172.35005) Full Text: DOI arXiv
Barles, Guy; Cardaliaguet, Pierre; Ley, Olivier; Monneau, Régis Global existence results and uniqueness for dislocation equations. (English) Zbl 1158.49029 SIAM J. Math. Anal. 40, No. 1, 44-69 (2008). MSC: 49L25 35F25 35A05 35D05 35B50 45G10 74E15 PDFBibTeX XMLCite \textit{G. Barles} et al., SIAM J. Math. Anal. 40, No. 1, 44--69 (2008; Zbl 1158.49029) Full Text: DOI arXiv
Barles, Guy; Imbert, Cyril Second-order elliptic integro-differential equations: viscosity solutions’ theory revisited. (English) Zbl 1155.45004 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 3, 567-585 (2008). Reviewer: Cornelis van der Mee (Cagliari) MSC: 45K05 45M10 49L25 45G10 PDFBibTeX XMLCite \textit{G. Barles} and \textit{C. Imbert}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 3, 567--585 (2008; Zbl 1155.45004) Full Text: DOI arXiv EuDML
Barles, G.; Chasseigne, E.; Imbert, C. On the Dirichlet problem for second-order elliptic integro-differential equations. (English) Zbl 1139.47057 Indiana Univ. Math. J. 57, No. 1, 213-246 (2008). Reviewer: Marlène Frigon (Montréal) MSC: 47N20 45K05 47G20 35D99 35J60 35J65 35J67 49L25 PDFBibTeX XMLCite \textit{G. Barles} et al., Indiana Univ. Math. J. 57, No. 1, 213--246 (2008; Zbl 1139.47057) Full Text: DOI
Barles, Guy; Perthame, Benoît Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics. (English) Zbl 1137.49027 Danielli, Donatella (ed.), Recent developments in nonlinear partial differential equations. Proceedings of the second symposium on analysis and PDEs, West Lafayette, IN, USA, June 7–10, 2004. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-3740-5/pbk). Contemporary Mathematics 439, 57-68 (2007). MSC: 49L25 35B25 92D15 92D25 PDFBibTeX XMLCite \textit{G. Barles} and \textit{B. Perthame}, Contemp. Math. 439, 57--68 (2007; Zbl 1137.49027)
Barles, Guy Some homogenization results for non-coercive Hamilton-Jacobi equations. (English) Zbl 1136.35004 Calc. Var. Partial Differ. Equ. 30, No. 4, 449-466 (2007). Reviewer: Fabio Paronetto (Lecce) MSC: 35B27 35F20 35F25 49L25 PDFBibTeX XMLCite \textit{G. Barles}, Calc. Var. Partial Differ. Equ. 30, No. 4, 449--466 (2007; Zbl 1136.35004) Full Text: DOI arXiv
Barles, Guy; Jakobsen, Espen R. Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations. (English) Zbl 1123.65096 Math. Comput. 76, No. 260, 1861-1893 (2007). Reviewer: Marius Ghergu (Dublin) MSC: 65M15 65M06 49L25 35K60 PDFBibTeX XMLCite \textit{G. Barles} and \textit{E. R. Jakobsen}, Math. Comput. 76, No. 260, 1861--1893 (2007; Zbl 1123.65096) Full Text: DOI arXiv
Barles, Guy; Ley, Olivier Nonlocal first-order Hamilton-Jacobi equations modelling dislocations dynamics. (English) Zbl 1109.35026 Commun. Partial Differ. Equations 31, No. 8, 1191-1208 (2006). Reviewer: Vasile Iftode (Bucureşti) MSC: 35F20 35D05 49L25 PDFBibTeX XMLCite \textit{G. Barles} and \textit{O. Ley}, Commun. Partial Differ. Equations 31, No. 8, 1191--1208 (2006; Zbl 1109.35026) Full Text: DOI arXiv
Barles, Guy; Da Lio, Francesca Local \(C^{0,\alpha }\) estimates for viscosity solutions of Neumann-type boundary value problems. (English) Zbl 1147.35312 J. Differ. Equations 225, No. 1, 202-241 (2006). MSC: 35J60 35B65 35J65 35J70 PDFBibTeX XMLCite \textit{G. Barles} and \textit{F. Da Lio}, J. Differ. Equations 225, No. 1, 202--241 (2006; Zbl 1147.35312) Full Text: DOI arXiv
Barles, Guy; Ramaswamy, Mythily Sufficient structure conditions for uniqueness of viscosity solutions of semilinear and quasilinear equations. (English) Zbl 1146.35326 NoDEA, Nonlinear Differ. Equ. Appl. 12, No. 4, 503-523 (2005). MSC: 35B50 35B05 35J61 35J62 35J70 PDFBibTeX XMLCite \textit{G. Barles} and \textit{M. Ramaswamy}, NoDEA, Nonlinear Differ. Equ. Appl. 12, No. 4, 503--523 (2005; Zbl 1146.35326) Full Text: DOI
Barles, Guy; Da Lio, Francesca On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions. (English) Zbl 1130.35047 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 22, No. 5, 521-541 (2005). MSC: 35J60 35B05 35B40 35J25 35K55 49L25 93E20 PDFBibTeX XMLCite \textit{G. Barles} and \textit{F. Da Lio}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 22, No. 5, 521--541 (2005; Zbl 1130.35047) Full Text: DOI arXiv Numdam EuDML
Barles, Guy; Jakobsen, Espen R. Error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations. (English) Zbl 1092.65077 SIAM J. Numer. Anal. 43, No. 2, 540-558 (2005). Reviewer: Dietrich Braess (Bochum) MSC: 65M15 35L70 49L25 65M06 PDFBibTeX XMLCite \textit{G. Barles} and \textit{E. R. Jakobsen}, SIAM J. Numer. Anal. 43, No. 2, 540--558 (2005; Zbl 1092.65077) Full Text: DOI
Barles, Guy; Da Lio, Francesca On the generalized Dirichlet problem for viscous Hamilton–Jacobi equations. (English) Zbl 1056.35071 J. Math. Pures Appl., IX. Sér. 83, No. 1, 53-75 (2004). Reviewer: Mersaid Aripov (Tashkent) MSC: 35K10 35K20 49L25 PDFBibTeX XMLCite \textit{G. Barles} and \textit{F. Da Lio}, J. Math. Pures Appl. (9) 83, No. 1, 53--75 (2004; Zbl 1056.35071) Full Text: DOI
Barles, Guy; Da Lio, Francesca A geometric approach to front propagation problems in bounded domains with Neumann-type boundary conditions. (English) Zbl 1046.35059 Interfaces Free Bound. 5, No. 3, 239-274 (2003). MSC: 35K57 35Q72 35B40 74N20 35K60 PDFBibTeX XMLCite \textit{G. Barles} and \textit{F. Da Lio}, Interfaces Free Bound. 5, No. 3, 239--274 (2003; Zbl 1046.35059) Full Text: DOI
Barles, Guy; Da Lio, Francesca Remarks on the Dirichlet and state-constraint problems for quasilinear parabolic equations. (English) Zbl 1073.35120 Adv. Differ. Equ. 8, No. 8, 897-922 (2003). Reviewer: Jorge Ferreira (São João del-Rei) MSC: 35K60 35K55 35B05 35B50 49L25 PDFBibTeX XMLCite \textit{G. Barles} and \textit{F. Da Lio}, Adv. Differ. Equ. 8, No. 8, 897--922 (2003; Zbl 1073.35120)
Barles, Guy; Biton, Samuel; Ley, Olivier Uniqueness for parabolic equations without growth condition and applications to the mean curvature flow in \(\mathbb R^2\). (English) Zbl 1028.35067 J. Differ. Equations 187, No. 2, 456-472 (2003). Reviewer: F.Tomi (Heidelberg) MSC: 35K55 53C44 35K15 PDFBibTeX XMLCite \textit{G. Barles} et al., J. Differ. Equations 187, No. 2, 456--472 (2003; Zbl 1028.35067) Full Text: DOI
Barles, Guy; Biton, Samuel; Ley, Olivier Quelques résultats d’unicité pour l’équation du mouvement par courbure moyenne dans \(\mathbb R^n\). (French. English summary) Zbl 1011.35082 ESAIM, Proc. 11, 1-12 (2002). MSC: 35K65 53C44 PDFBibTeX XMLCite \textit{G. Barles} et al., ESAIM, Proc. 11, 1--12 (2002; Zbl 1011.35082) Full Text: DOI
Barles, Guy; Jakobsen, Espen Robstad On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations. (English) Zbl 0998.65067 M2AN, Math. Model. Numer. Anal. 36, No. 1, 33-54 (2002). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 65K10 49L20 49L25 PDFBibTeX XMLCite \textit{G. Barles} and \textit{E. R. Jakobsen}, M2AN, Math. Model. Numer. Anal. 36, No. 1, 33--54 (2002; Zbl 0998.65067) Full Text: DOI Numdam EuDML
Barles, Guy; Tourin, Agnès Commutation properties of semigroups for first-order Hamilton-Jacobi equations and application to multi-time equations. (English) Zbl 1044.49022 Indiana Univ. Math. J. 50, No. 4, 1523-1544 (2001). MSC: 49L25 35F20 47H20 91B02 PDFBibTeX XMLCite \textit{G. Barles} and \textit{A. Tourin}, Indiana Univ. Math. J. 50, No. 4, 1523--1544 (2001; Zbl 1044.49022) Full Text: DOI Link
Barles, G.; Busca, Jérôme Existence and comparison results for fully nonlinear degenerate elliptic equations without Zeroth-order term. (English) Zbl 0997.35023 Commun. Partial Differ. Equations 26, No. 11-12, 2323-2337 (2001). MSC: 35J70 35J60 35B05 35D05 PDFBibTeX XMLCite \textit{G. Barles} and \textit{J. Busca}, Commun. Partial Differ. Equations 26, No. 11--12, 2323--2337 (2001; Zbl 0997.35023) Full Text: DOI
Barles, G.; Souganidis, P. E. Space-time periodic solutions and long-time behavior of solutions to quasi-linear parabolic equations. (English) Zbl 0986.35047 SIAM J. Math. Anal. 32, No. 6, 1311-1323 (2001). Reviewer: Jiaqi Mo (Wuhu) MSC: 35K55 35B10 35K45 35K65 35B40 PDFBibTeX XMLCite \textit{G. Barles} and \textit{P. E. Souganidis}, SIAM J. Math. Anal. 32, No. 6, 1311--1323 (2001; Zbl 0986.35047) Full Text: DOI
Barles, G.; Souganidis, Panagiotis E. On the large time behavior of solutions of Hamilton-Jacobi equations. (English) Zbl 0960.70015 SIAM J. Math. Anal. 31, No. 4, 925-939 (2000). Reviewer: Oleg Titow (Berlin) MSC: 70H20 35Q72 PDFBibTeX XMLCite \textit{G. Barles} and \textit{P. E. Souganidis}, SIAM J. Math. Anal. 31, No. 4, 925--939 (2000; Zbl 0960.70015) Full Text: DOI
Barles, Guy; Rouy, Elisabeth; Souganidis, Panagiotis E. Remarks on the Dirichlet problem for quasilinear elliptic and parabolic equations. (English) Zbl 0928.35049 McEneaney, William M. (ed.) et al., Stochastic analysis, control, optimization and applications. A volume in honor of Wendell H. Fleming, on the occasion of his 70th birthday. Boston: Birkhäuser, 209-222 (1999). Reviewer: Lars Grüne (Frankfurt) MSC: 35J60 49L25 35K55 35A05 PDFBibTeX XMLCite \textit{G. Barles} et al., in: Stochastic analysis, control, optimization and applications. A volume in honor of Wendell H. Fleming, on the occasion of his 70th birthday. Boston: Birkhäuser. 209--222 (1999; Zbl 0928.35049)
Barles, G.; Rouy, E. A strong comparison result for the Bellman equation arising in stochastic exit time control problems and its applications. (English) Zbl 0919.35009 Commun. Partial Differ. Equations 23, No. 11-12, 1995-2033 (1998). Reviewer: W.Kotarski (Sosnowiec) MSC: 35B05 35B45 35R60 60H15 PDFBibTeX XMLCite \textit{G. Barles} and \textit{E. Rouy}, Commun. Partial Differ. Equations 23, No. 11--12, 1995--2033 (1998; Zbl 0919.35009) Full Text: DOI
Barles, Guy; Soner, Halil Mete Option pricing with transaction costs and a nonlinear Black-Scholes equation. (English) Zbl 0915.35051 Finance Stoch. 2, No. 4, 369-397 (1998). MSC: 35K55 91G20 93E20 PDFBibTeX XMLCite \textit{G. Barles} and \textit{H. M. Soner}, Finance Stoch. 2, No. 4, 369--397 (1998; Zbl 0915.35051) Full Text: DOI
Barles, Guy; Buckdahn, Rainer; Pardoux, Etienne Backward stochastic differential equations and integral-partial differential equations. (English) Zbl 0878.60036 Stochastics Stochastics Rep. 60, No. 1-2, 57-83 (1997). Reviewer: J.-P.Lepeltier (Le Mans) MSC: 60H10 60G44 35K55 PDFBibTeX XMLCite \textit{G. Barles} et al., Stochastics Stochastics Rep. 60, No. 1--2, 57--83 (1997; Zbl 0878.60036) Full Text: DOI
Barles, Guy; Blanc, Alain-Philippe Large deviations estimates for the exit probabilities of a diffusion process through some vanishing parts of the boundary. (English) Zbl 1023.60502 Adv. Differ. Equ. 2, No. 1, 39-84 (1997). MSC: 60F10 35B05 35R60 49L25 60J60 PDFBibTeX XMLCite \textit{G. Barles} and \textit{A.-P. Blanc}, Adv. Differ. Equ. 2, No. 1, 39--84 (1997; Zbl 1023.60502)
Barles, G. Convergence of numerical schemes for degenerate parabolic equations arising in finance theory. (English) Zbl 0898.90015 Rogers, L. C. G. (ed.) et al., Numerical methods in finance. Session at the Isaac Newton Institute, Cambridge, GB, 1995. Cambridge: Cambridge Univ. Press. 1-21 (1997). MSC: 91B28 65N12 35K57 35J60 PDFBibTeX XMLCite \textit{G. Barles}, in: Numerical methods in finance. Session at the Isaac Newton Institute, Cambridge, GB, 1995. Cambridge: Cambridge Univ. Press. 1--21 (1997; Zbl 0898.90015)
Barles, Guy; Georgelin, Christine A simple proof of convergence for an approximation scheme for computing motions by mean curvature. (English) Zbl 0831.65138 SIAM J. Numer. Anal. 32, No. 2, 484-500 (1995). Reviewer: B.Burrows (Stafford) MSC: 65Z05 65M12 35R35 35K65 53C21 76T99 PDFBibTeX XMLCite \textit{G. Barles} and \textit{C. Georgelin}, SIAM J. Numer. Anal. 32, No. 2, 484--500 (1995; Zbl 0831.65138) Full Text: DOI HAL
Barles, G.; Burdeau, J. The Dirichlet problem for semilinear second-order degenerate elliptic equations and applications to stochastic exit time control problems. (English) Zbl 0826.35038 Commun. Partial Differ. Equations 20, No. 1-2, 129-178 (1995). Reviewer: B.Kvedaras (Vilnius) MSC: 35J70 35J60 60H15 PDFBibTeX XMLCite \textit{G. Barles} and \textit{J. Burdeau}, Commun. Partial Differ. Equations 20, No. 1--2, 129--178 (1995; Zbl 0826.35038) Full Text: DOI
Barles, Guy Viscosity solutions of Hamilton-Jacobi equations. (Solutions de viscosité des équations de Hamilton-Jacobi.) (French) Zbl 0819.35002 Mathématiques & Applications (Berlin). 17. Paris: Springer-Verlag. ix, 194 p. (1994). Reviewer: S.Lenhart (Knoxville) MSC: 35-02 35F20 35B25 PDFBibTeX XMLCite \textit{G. Barles}, Solutions de viscosité des équations de Hamilton-Jacobi. Paris: Springer-Verlag (1994; Zbl 0819.35002)
Barles, Guy Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations: A guided visit. (English) Zbl 0816.35081 Nonlinear Anal., Theory Methods Appl. 20, No. 9, 1123-1134 (1993). Reviewer: G.Aniculaesei (Iaşi) MSC: 35L60 70H20 PDFBibTeX XMLCite \textit{G. Barles}, Nonlinear Anal., Theory Methods Appl. 20, No. 9, 1123--1134 (1993; Zbl 0816.35081) Full Text: DOI
Barles, G.; Soner, H. M.; Souganidis, P. E. Front propagation and phase field theory. (English) Zbl 0785.35049 SIAM J. Control Optimization 31, No. 2, 439-469 (1993). MSC: 35K57 53A10 35A05 PDFBibTeX XMLCite \textit{G. Barles} et al., SIAM J. Control Optim. 31, No. 2, 439--469 (1993; Zbl 0785.35049) Full Text: DOI Link
Barles, G.; Bronsard, L.; Souganidis, P. E. Front propagation for reaction-diffusion equations of bistable type. (English) Zbl 0794.35076 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 9, No. 5, 479-496 (1992). Reviewer: S.Jimbo (Tsushima) MSC: 35K57 35B25 35B60 49L25 PDFBibTeX XMLCite \textit{G. Barles} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 9, No. 5, 479--496 (1992; Zbl 0794.35076) Full Text: DOI Numdam EuDML
Barles, G. Interior gradient bounds for the mean curvature equation by viscosity solutions methods. (English) Zbl 0735.35020 Differ. Integral Equ. 4, No. 2, 263-275 (1991). Reviewer: G.M.Lieberman (Ames) MSC: 35B45 35J60 35D40 PDFBibTeX XMLCite \textit{G. Barles}, Differ. Integral Equ. 4, No. 2, 263--275 (1991; Zbl 0735.35020)
Barles, G.; Lions, P. L. Fully nonlinear Neumann type boundary conditions for first-order Hamilton-Jacobi equations. (English) Zbl 0736.35023 Nonlinear Anal., Theory Methods Appl. 16, No. 2, 143-153 (1991). Reviewer: N.Jacob (Erlangen) MSC: 35F30 70H20 49L25 35A05 PDFBibTeX XMLCite \textit{G. Barles} and \textit{P. L. Lions}, Nonlinear Anal., Theory Methods Appl. 16, No. 2, 143--153 (1991; Zbl 0736.35023) Full Text: DOI
Barles, G. A weak Bernstein method for fully non-linear elliptic equations. (English) Zbl 0733.35014 Differ. Integral Equ. 4, No. 2, 241-262 (1991). Reviewer: J. E. Bouillet (Buenos Aires) MSC: 35B45 35J65 35B50 35D40 PDFBibTeX XMLCite \textit{G. Barles}, Differ. Integral Equ. 4, No. 2, 241--262 (1991; Zbl 0733.35014)
Barles, G. Regularity results for first order Hamilton-Jacobi equations. (English) Zbl 0739.35012 Differ. Integral Equ. 3, No. 1, 103-125 (1990). Reviewer: J.Schmeelk (Richmond) MSC: 35F25 35D10 35F30 35B05 70H20 35B65 PDFBibTeX XMLCite \textit{G. Barles}, Differ. Integral Equ. 3, No. 1, 103--125 (1990; Zbl 0739.35012)
Barles, G.; Evans, L. C.; Sougandis, P. E. Wavefront propagation for reaction-diffusion systems of PDE. (English) Zbl 0749.35015 Duke Math. J. 61, No. 3, 835-858 (1990). Reviewer: L.Simon (Budapest) MSC: 35K57 35K55 35B40 35K45 PDFBibTeX XMLCite \textit{G. Barles} et al., Duke Math. J. 61, No. 3, 835--858 (1990; Zbl 0749.35015) Full Text: DOI
Barles, G. An approach of deterministic control problems with unbounded data. (English) Zbl 0717.49021 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 7, No. 4, 235-258 (1990). MSC: 49L99 49L25 PDFBibTeX XMLCite \textit{G. Barles}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 7, No. 4, 235--258 (1990; Zbl 0717.49021) Full Text: DOI Numdam EuDML
Barles, G.; Perthame, B. Comparison principle for Dirichlet-type Hamilton-Jacobi equations and singular perturbations of degenerated elliptic equations. (English) Zbl 0691.49028 Appl. Math. Optimization 21, No. 1, 21-44 (1990). MSC: 49L99 35B05 35B25 PDFBibTeX XMLCite \textit{G. Barles} and \textit{B. Perthame}, Appl. Math. Optim. 21, No. 1, 21--44 (1990; Zbl 0691.49028) Full Text: DOI
Barles, G.; Perthame, B. Exit time problems in optimal control and vanishing viscosity method. (English) Zbl 0674.49027 SIAM J. Control Optimization 26, No. 5, 1133-1148 (1988). Reviewer: R.Gonzalez MSC: 49L99 35F30 91A23 49K35 49J40 91A99 49L20 35B25 PDFBibTeX XMLCite \textit{G. Barles} and \textit{B. Perthame}, SIAM J. Control Optim. 26, No. 5, 1133--1148 (1988; Zbl 0674.49027) Full Text: DOI
Barles, G.; Lions, P. L. Remarks on existence and uniqueness results for first-order Hamilton-Jacobi equations. (English) Zbl 0644.35015 Contributions to nonlinear partial differential equations, Vol. II, Proc. 2nd Franco-Span. Colloq., Paris 1985, Pitman Res. Notes Math. Ser. 155, 4-15 (1987). Reviewer: E.Barron MSC: 35F20 35D05 PDFBibTeX XML
Barles, G. Uniqueness for first-order Hamilton-Jacobi equations and Hopf formula. (English) Zbl 0632.35009 J. Differ. Equations 69, 346-367 (1987). Reviewer: S.M.Lenhart MSC: 35F30 35A05 PDFBibTeX XMLCite \textit{G. Barles}, J. Differ. Equations 69, 346--367 (1987; Zbl 0632.35009) Full Text: DOI
Barles, G.; Perthame, B. Discontinuous solutions of deterministic optimal stopping time problems. (English) Zbl 0629.49017 RAIRO, Modélisation Math. Anal. Numér. 21, 557-579 (1987). Reviewer: E.Barron MSC: 49L20 35F20 49J40 60G40 35D05 49J45 PDFBibTeX XMLCite \textit{G. Barles} and \textit{B. Perthame}, RAIRO, Modélisation Math. Anal. Numér. 21, 557--579 (1987; Zbl 0629.49017) Full Text: DOI EuDML
Barles, G. Asymptotic behavior of viscosity solutions of first order Hamilton-Jacobi equations. (English) Zbl 0637.49014 Ric. Mat. 34, 227-260 (1985). Reviewer: R.Gonzales MSC: 49L99 35B40 35F20 PDFBibTeX XMLCite \textit{G. Barles}, Ric. Mat. 34, 227--260 (1985; Zbl 0637.49014)
Barles, G. Remarques sur des résultats d’existence pour les équations de Hamilton-Jacobi du premier ordre. (French) Zbl 0573.35010 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 2, 21-32 (1985). Reviewer: M.Biroli MSC: 35F25 35D05 35B05 35F20 PDFBibTeX XMLCite \textit{G. Barles}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 2, 21--32 (1985; Zbl 0573.35010) Full Text: DOI Numdam EuDML
Barles, G. Deterministic impulse control problems. (English) Zbl 0571.49020 SIAM J. Control Optimization 23, 419-432 (1985). Reviewer: R.Gonzales MSC: 49L20 49J40 49L99 35D05 35D10 35J85 PDFBibTeX XMLCite \textit{G. Barles}, SIAM J. Control Optim. 23, 419--432 (1985; Zbl 0571.49020) Full Text: DOI
Barles, G. Existence results for first order Hamilton Jacobi equations. (English) Zbl 0574.70019 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 1, 325-340 (1984). Reviewer: P.L.Lions MSC: 70H20 35F30 49L99 PDFBibTeX XMLCite \textit{G. Barles}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 1, 325--340 (1984; Zbl 0574.70019) Full Text: DOI Numdam EuDML