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Site du département Mathématiques Appliquées de l'INSA Rennes
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Site du Master Franco-Vietnamien de Mathématiques Appliquées
commun à Vietnam National University Ho Chi Minh City (HCMUS), Universités Lorraine, Orléans, Paris 13, Rennes 1, Tours et École Polytechnique.

Domaines de recherche /Research topics

Équations aux dérivées partielles non-linéaires /Nonlinear partial differential equations

Solutions de viscosité /Viscosity solutions

Équations de Hamilton-Jacobi, contrôle optimal, jeux à champ moyen /Hamilton-Jacobi equations, Optimal control, Mean Field Games

Équations géométriques, mouvement par courbure moyenne, dislocations /Geometric equations, mean curvature motion, dislocations

Équations non-locales intégro-différentielles /Nonlocal PDE, integro-differential operators

Comportement asymptotique pour Hamilton-Jacobi /Large time behavior of solutions to HJ equations

Analyse convexe et optimisation /Convex analysis and Optimization

Editorial Board

Member of the editorial board of Nonlinear Differential Equations and Applications NoDEA

Publications

Preprints

[40] Adina Ciomaga, Minh Le, Olivier Ley, Erwin Topp: Comparison principle for general nonlocal Hamilton-Jacobi equations with superlinear gradient
  Preprint, 2024. (pdf) (on HAL-server).

[39] Aris Daniilidis, Mounir Haddou, Tri Minh Le, Olivier Ley: Solving Nonlinear Absolute Value Equations
  Preprint, 2024. (pdf) (on HAL-server).

[38] Jules Berry, Olivier Ley, Francisco Silva: Approximation and perturbations of stable solutions to a stationary mean field game system
  Preprint, 2024. (pdf) (on HAL-server).

Parues ou à paraître

[37] Aris Daniilidis, Mounir Haddou, Olivier Ley: A convex function satisfying the Lojasiewicz inequality but failing the gradient conjecture both at zero and infinity
  Bull. Lond. Math. Soc. 54 (2), 590-608, 2022. (pdf) (on HAL-server).

[36] Olivier Ley, Erwin Topp, Miguel Yangari: Some results for the large time behavior of Hamilton-Jacobi Equations with Caputo Time Derivative.
  Discrete Contin. Dyn. Syst. Ser. A. 41 (8), 3555-3577, 2021. (pdf) (on HAL-server).

[35] Yves Achdou, Manh-Khang Dao, Olivier Ley, Nicoletta Tchou : Finite Horizon Mean Field Games on Networks.
  Calc. Var. Partial Differential Equations 59, No 157, 34 pp, 2020. (pdf) (on HAL-server).

[34] Yves Achdou, Manh-Khang Dao, Olivier Ley, Nicoletta Tchou : A Class of Infinite Horizon Mean Field Games on Networks.
  Netw. Heterog. Media. 14, 537-566, 2019. (pdf) (on HAL-server).

[33] Guy Barles, Olivier Ley, Thi-Tuyen Nguyen, Thanh Viet Phan : Large time Behavior of unbounded solutions of first-order Hamilton-Jacobi in R^N.
  Asymptotic Anal. 112, 1-22, 2019. (pdf) (on HAL-server).

[32] Emmanuel Chasseigne, Olivier Ley, Thi-Tuyen Nguyen : A priori Lipschitz estimates for solutions of local and nonlocal Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator.
  Rev. Mat. Iberoam. 35, 1415-1449, 2019. (pdf) (on HAL-server).

[31] Aris Daniilidis, Mounir Haddou, Erwan Le Gruyer, Olivier Ley : Explicit formulas for C1,1 Glaeser-Whitney extensions of 1-fields in Hilbert spaces.
  Proc. Amer. Math. Soc. 146, 4487-4495, 2018. (pdf) (on HAL-server).

[30] Olivier Ley, Vinh Duc Nguyen : Lipschitz regularity results for nonlinear strictly elliptic equations and applications
  J. Differential Equations 263, 4324-4354, 2017. (pdf) (on HAL-server).

[29] Guy Barles, Olivier Ley, Erwin Topp: Lipschitz regularity for integro-differential equations with coercive Hamiltonians and applications to large time behavior
  Nonlinearity 30, 703-734, 2017. (pdf) (on HAL-server).

[28] Giulio Galise, Shigeaki Koike, Olivier Ley, Antonio Vitolo : Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term
  J. Math. Anal. Appl. 441, 194-210, 2016. (pdf) (on HAL-server).

[27] Olivier Ley, Vinh Duc Nguyen : Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems
  Nonlinear Analysis 130, 76-101, 2016. (pdf) (on HAL-server).

[26] Guy Barles, Shigeaki Koike, Olivier Ley, Erwin Topp : Regularity Results and Large Time Behavior for Integro-Differential Equations with Coercive Hamiltonians
  Calc. Var. Partial Differential Equations 54, 539-572, 2015. (pdf) (on HAL-server).

[25] Olivier Ley, Vinh Duc Nguyen : Large time behavior for some nonlinear degenerate parabolic equations
  J. Math. Pures Appl. 102, 293-314, 2014. (pdf) (on HAL-server).

[24] Fabio Camilli, Olivier Ley, Paola Loreti, Vinh Duc Nguyen : Large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations
  NoDEA Nonlinear Differential Equations Appl. 19, 719-749, 2012. (pdf) (on HAL-server).

[23] Guy Barles, Olivier Ley et Hiroyoshi Mitake : Short time uniqueness results for solutions of nonlocal and non-monotone geometric equations
  Math. Ann. 352, 409-451, 2012. (pdf) (on HAL-server).

[22] Pierre Cardaliaguet, Olivier Ley et Aurélien Monteillet : Viscosity solutions for a polymer crystal growth model.
  Indiana Univ. Math. J. 60, 895-936, 2011. (pdf) (on HAL-server).

[21] Shigeaki Koike and Olivier Ley : Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms
  J. Math. Anal. Appl. 381, 110-120, 2011. (pdf) (on HAL-server).

[20] Aris Daniilidis, Olivier Ley and Stéphane Sabourau : Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions.
  J. Math. Pures Appl. 94, 183-199, 2010. (pdf) (on HAL-server).

[19] Francesca Da Lio et Olivier Ley : Uniqueness results for convex Hamilton-Jacobi equations under p>1 growth conditions on data.
  Appl. Math. Optim. 63(3), 309-339, 2011. (pdf) (on HAL-server).

[18] Jérôme Bolte, Aris Daniilidis, Olivier Ley and Laurent Mazet : Characterizations of Lojasiewicz inequalities: Subgradient flows, talweg, convexity.
  Trans. Amer. Math. Soc. 362 (6), 3319-3363, 2010. (pdf) (on HAL-server).

[17] Guy Barles, Pierre Cardaliaguet, Olivier Ley et Aurélien Monteillet : Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations
  Nonlinear Analysis. Theory, Methods and Applications, 71 (7-8), 2801-2810, 2009. (pdf) (on HAL-server).

[16'] Olivier Ley : Nonlocal Hamilton-Jacobi equations related to dislocation dynamics and a FitzHugh-Nagumo system.
  Proceedings of the ``Viscosity solutions of differential equations and related topics'' (Kyoto 2008) RIMS Kokyuroku 1651, 2009. (pdf) (on HAL-server).

[16] Guy Barles, Pierre Cardaliaguet, Olivier Ley et Aurélien Monteillet : Uniqueness Results for Nonlocal Hamilton-Jacobi Equations.
  Journal of Functional Analysis 257 (5), 1261-1287, 2009. (pdf) (on HAL-server).

[HDR] Olivier Ley : Évolution de fronts avec vitesse non-locale et \'equations de Hamilton-Jacobi.
  Habilitation à Diriger des Recherches, Université de Tours, 8 décembre 2008. (pdf)

[15] Fabio Camilli, Olivier Ley, Paola Loreti : Homogenization of monotone systems of Hamilton-Jacobi equations
  ESAIM: Control, Optim. Calc. Var. 16, 58-76, 2010. (pdf) (on HAL-server).

[14] Olivier Ley : Weak solutions for dislocation type equations
  Gakuto International Series, Mathematical Sciences and Applications 30, 117-132, 2008. (pdf) (on HAL-server).

[13] Guy Barles, Pierre Cardaliaguet, Olivier Ley et Régis Monneau : Global existence results and uniqueness for dislocation equations.
  SIAM J. Math. Anal. 40, 44-69, 2008 (pdf) (on HAL-server).

[12] Samuel Biton, Pierre Cardaliaguet et Olivier Ley : Non fattening condition for the generalized evolution by mean curvature and applications.
  Interfaces Free Bound. 10, 1-14, 2008. (Résumé)- (pdf)

[11] Pierre Cardaliaguet et Olivier Ley : On the energy of a flow arising in shape optimization.
  Interfaces Free Bound. 10, 221-241, 2008. (pdf) (on HAL-server).

[10'] Olivier Ley : Geometric flows and Bernoulli problems.
  Proceedings of the 29th Sapporo Symposium on PDE, Hokkaido University Technical Report Series in Mathematics, 84 : 1-8, 2004.   (pdf)

[10] Pierre Cardaliaguet et Olivier Ley : Some flows in shape optimization.
    Arch. Rational Mech. Anal. 183 (1), 21-58, 2007. (pdf) (on HAL-server).

[9] Francesca Da Lio et Olivier Ley : Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications.
  SIAM J. Control Optim., 45 (1) : 74-106, 2006. (pdf) (on HAL-server).

[8] Guy Barles et Olivier Ley : Nonlocal first-order Hamilton-Jacobi equations modelling dislocations dynamics.
    Comm. Partial Differential Equations, 31 (8) : 1191-1208, 2006. (pdf) (on HAL-server).

[proc1] Olivier Ley : Motion by mean curvature and level-set approach.
  Proceedings of a talk given at Muroran Institute of Technology (Japan), July 2004.   (pdf)

[7] Samuel Biton, Emmanuel Chasseigne et Olivier Ley : Uniqueness without growth condition for the mean curvature equation with radial initial data.
  Comm. Partial Differential Equations, 28 (9-10) : 1503-1526, 2003.   (Résumé)- (pdf)

[6] Guy Barles, Samuel Biton, Mariane Bourgoing et Olivier Ley : Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods.
  Calc. Var. Partial Differential Equations 18 : 159-179, 2003. (ps)

[5] Guy Barles, Samuel Biton et Olivier Ley : Uniqueness for parabolic equations without growth condition and applications to the mean curvature flow in R^2.
  J. Differential Equations 187 : 456-472, 2003.   (ps)

[4] Guy Barles, Samuel Biton et Olivier Ley : A Geometrical Approach to the Study of Unbounded Solutions of Quasilinear Parabolic Equations.
  Arch. Rational Mech. Anal. 162 (4) : 287-325, 2002.   (Résumé)- (pdf)

[3] Guy Barles, Samuel Biton et Olivier Ley : Quelques résultats d'unicité pour l'équation de mouvement par courbure moyenne dans R^N.
  ESAIM: Proceedings, Actes du 32eme Congrès d'Analyse Numérique : Canum 2000, 8, 2002.  (Résumé)- (pdf)

[2] Olivier Ley : A counter-example to the characterization of the discontinuous value function of control problems with reflection.
  C. R. Acad. Sci. Paris, Ser. I, 335 : 469-473, 2002.   (Résumé)- (pdf)

[THESE] Olivier Ley : Thèse de doctorat, Université de Tours, 2001.
  (Résumé)- (Abstract)- (ps.gz)

[1] Olivier Ley : Lower-bound gradient estimates for first-order Hamilton-Jacobi equations and applications to the regularity of propagating fronts.
  Adv. Differential Equations, 6 (5) : 547-576, 2001.   (Résumé)- (pdf)-(ps)