Cyril Imbert

UMR 8050, Université Paris-Est Créteil
Laboratoire d'Analyse et de Mathématiques Appliquées
61, avenue du Général de Gaulle
94010 Créteil, France

Bureau : P3 440 (voir ici pour venir)
Téléphone : (33) 1 45 17 16 52
Fax : (33) 1 45 17 16 49
Courriel : prenom.nom (at) u-pec.fr
Blog : http://blog-cyrilimbert.net

Curriculum Vitae

You can get a pdf file or see it on my blog

Event

Nonlocal Operators: Analysis, Probability, Geometry and Applications July 9th - 14th, 2012 ZiF Bielefeld A summer school will preceed this workshop, with Lectures by L. Silvestre and Z.-Q. Chen

Research

I am interested in nonlinear partial differential equations.

Please note that the pdf-files of the articles posted on this page may differ from the journal publications.

Articles

• Convex Analysis techniques for Hopf-Lax formulae in Hamilton-Jacobi equations. Journal of Nonlinear and Convex Analysis Vol 2, No 3 (2001) pp. 333-343
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• Support functions of Clarke's generalized jacobian and of its plenary hull. Nonlinear Analysis, Theory, Methods and Applications, Vol 29, No 8 (2002) pp. 1111-1125
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• Some regularity results for anisotropic motion of fronts. Differential and Integral Equations, Vol 15, No 10 (2002) pp. 1263-1271
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• Avec Michel Volle. On vectorial Hamiton-Jacobi equations. Control and Cybernetics, Vol 31, No 3 (2002) pp. 493-506
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• Avec J. Vovelle. A kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications. SIAM – Mathematical Analysis, Vol 36, Issue 1 (2004), pp. 214-232
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• Avec J. Droniou et J. Vovelle. An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions. Annales de l’Institut Henri Poincaré – Analyse non linéaire, Vol 21, Issue 5 (2004), pp. 689-714
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• A non-local regularization of first order Hamilton-Jacobi equations. Journal of Differential Equations, Vol 211, Issue 1 (2005), pp. 218-246
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• Convexity of solutions and C^1,1 estimates for fully nonlinear elliptic equations. Journal de Mathématiques Pures et Appliquées, Vol 85, Issue 6 (2006), pp. 791-807
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• Avec J. Droniou. Fractal first order partial differential equations. Archive for Rational Mechanics and Analysis, Vol 182, No 2 (2006), pp. 299-331
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• Avec R. Monneau et E. Rouy. Homogenization of first order equations with (u/ε)-periodic Hamiltonians. Part II: application to dislocation dynamics. Communications in PDEs (2008), Volume 33, No 3, 479 — 516
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• Avec G. Barles. Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions’ Theory Revisited. Annales de l’IHP (2008), Volume 25, No 3, Pages 567-585
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• Avec R. Monneau. Homogenization of first order equations with (u/ε)-periodic Hamiltonians. Part I: local equations. Archive for Rational Mechanics and Analysis 187 (2008), 49-89
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• Avec G. Barles et E. Chasseigne. The Dirichlet problem for second-order elliptic integro-differential equations. Indiana Univ. Math. J. (2008), Volume 57, No 1, 213-146
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• Avec I. Gentil. The Lévy-Fokker-Planck equation: Φ-entropies and convergence to equilibrium. Asymptotic Analysis (2008), Vol 59, No 3-4, 125-138
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• Avec N. Alibaud. Fractional semi-linear parabolic equations with unbounded data. Transations of the American Mathematical Society 361 (2009), 2527-2566
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• Avec N. Forcadel et R. Monneau. Homogenization of the fully overdamped Frenkel-Kontorova models. J. Differential Equations 246 (2009), 1057-1097
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• Avec N. Forcadel et R. Monneau. Homogenization of some particle systems with two-body interactions and of the dislocation dynamics. Discrete and Continuous Dynamical Systems – Serie A 23 (2009), no 3, 785-826
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• Level set approach for fractional mean curvature flows. Interfaces and Free Boundaries (2009), Vol 11, Issue 1, 153-176
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• Avec G. Barles et E. Chasseigne. Hölder continuity of solutions of second-order elliptic integro-differential equations. Journal of the European Mathematical Society, Vol 13, Issue 1, pp. 1-26 (2011)
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• Avec B. Bouchard et R. Elie. Optimal control under stochastic target constraints. SIAM J. Control Optim. Volume 48, Issue 5, pp. 3501-3531 (2010)
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• Avec N. Alibaud et G. Karch. Asymptotic properties of entropy solutions to fractal Burgers equations. SIAM J. Math. Anal. Volume 42, Issue 1, pp. 354-376 (2010)
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• Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations. Journal of Differential Equations Vol 250, Issue 3 (2011), 1325–1766
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• Avec S. Serfaty. Repeated games for eikonal equations, integral curvature flows and integro-differential parabolic equations. Discrete Contin. Dyn. Syst. 29, 4 (2011), 1517-1552
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• Avec N. Forcadel et R. Monneau. Homogenization of accelerated Frenkel-Kontorova models with n types of particles. Trans. Am. Math. Soc. (à paraître)
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• Avec A. Mellet. Existence of solutions for a higher order non-local equation appearing in crack dynamics. Nonlinearity 24 (2011) 3487 3514
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• Avec R. Monneau et H. Zidani. A Hamilton-Jacobi approach to junction problems and application to traffic flows. ESAIM: Control, Optim. and Calc. Var. (à paraître)
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• Avec A. Mellet. Electrified thin films: Global existence of non-negative solutions. Annales de l'IHP, analyse non-linéaire (à paraître)
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• Avec G. Barles, E. Chasseigne et A. Ciomaga. Lipschitz regularity of solutions for mixed integro-differential equations. Journal of Differential Equations Vol 252 (2012), 6012–6060
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Prépublications

• Avec T. Souganidis. Phasefield theory for fractional diffusion-reaction equations and applications.
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• Avec N. Forcadel et R. Monneau. Uniqueness and existence of spirals moving by forced mean curvature motion.
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• Avec L. Silvestre. C^1,α regularity of solutions of degenerate fully non-linear elliptic equations.
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Contribution à ouvrage

• Avec N. Forcadel et R. Monneau. Viscosity solutions for particle systems and homogenization of dislocation dynamics.
  On the notions of solution to nonlinear elliptic problems: results and developments”, Quaderni di Matematica, 23. Department of Mathematics, Seconda Universita di Napoli, Caserta, 2008.
  Editeurs A. Alvino, A. Mercaldo, F. Murat, I. Peral

Notes et Proceedings

• Avec J.-B. Hiriart-Urruty. Les fonctions d’appui de la jacobienne généralisiée de Clarke et de son enveloppe plénèire. C. R. Acad. Sci. Paris Sér. I Math., Vol 326 No 11 (1998), pp. 1275-1278
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• Avec I. Gentil. Logarithmic Sobolev inequalities: regularizing effect of Lévy operators and asymptotic convergence in the Lévy-Fokker-Planck equation. Stochastics An International Journal of Probability and Stochastic Processes, 81:3, 401-414
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• Avec P. Biler et G. Karch. Barenblatt profiles for a nonlocal porous medium equation. C. R. Acad. Sci. Paris, Ser. I 349 (2011) 641-645.
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