Publications

Prépublications

  • Avec F. Golse et A. F. Vasseur. Local regularity for the space homogeneous Landau equation with very soft potentials. hal | arxiv

À paraître

  • Avec F. Golse, M. P. Gualdani, A. F. Vasseur. Partial Regularity in Time for the Space Homogeneous Landau Equation with Coulomb Potential. Annales scientifiques de l’ENS. hal | arxiv
  • Avec J. Guerand. Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations. Journal de l’institut mathématique de Jussieu. hal | arxiv

2022

  • Avec L. Silvestre. Global regularity estimates for the Boltzmann equation without cut-off. Journal of the Am. Math. Soc. Vol 35, No. 3, 625–703. hal | arxiv

2021

  • Avec L. Silvestre. The Schauder estimate for kinetic integral equations. Analysis and PDE. Vol. 14, No. 1, 171–204. hal | arxiv | doi
  • Avec C. Mouhot. The Schauder estimate in kinetic theory with application to a toy nonlinear model. Annales Henri Lebesgue, Vol. 4, pp. 369-405. hal | arxiv | doi

2020

  • Avec L. Silvestre. Regularity for the Boltzmann equation conditional to macroscopic bounds. EMS Surv. Math. Sci. 7 (2020), 117–172. hal | arxiv | doi
  • Avec R. Tarhini et F. Vigneron. Regularity of solutions of a fractional porous medium equation. Interfaces and free boundaries.Volume 22, Issue 4. hal | arxiv | doi
  • Avec C. Mouhot et L. Silvestre. Gaussian lower bounds for the Boltzmann equation without cut-off. SIAM J. Math. Anal. 52, no. 3, 2930–2944. hal | arxiv | doi
  • Avec L. Silvestre. The weak Harnack inequality for the Boltzmann equation without cut-off. Journal of the European Mathematical Society. Volume 22, Issue 2, pp. 507–592. doi | hal | arxiv | video
  • Avec C. Mouhot et L. Silvestre. Decay estimates for large velocities in the Boltzmann equation without cut-off. Journal de l’École Polytechnique — Mathématiques, Volume 7, p. 143-184. Journal | doi | hal | arxiv

2019

  • Avec T. Jin et L. Silvestre. Hölder gradient estimates for a class of singular or degenerate parabolic equations. Advances in Nonlinear Analysis, 8(1), pp. 845-867. doi | hal | arxiv | pdf
  • Avec F. Golse, C. Mouhot et A. F. Vasseur. Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. PP. 253-295 | Vol. XIX, issue 1. doi | hal | arxiv | video

2018

  • Avec G. Barles, A. Briani et E. Chasseigne.  Flux-limited and classical viscosity solutions for regional control problems. ESAIM:COCV, Vol. 24, pp. 1881–1906. doi | hal | arxiv
  • Avec T. Jin et R. Shvydkoy. Schauder estimates for an integro-differential equation with applications to a nonlocal Burgers equation. Annales de la Faculté des Sciences de Toulouse . Sér. 6, 27 no. 4 (2018), p. 667-677. doi | hal | arxiv

2017

  • Avec V. D. Nguyen. Generalized junction conditions for degenerate parabolic equations. Calculus of Variations and PDE’s, 56: 157. doi | hal | arxiv
  • Avec R. Monneau. Quasi-convex Hamilton-Jacobi equations posed on junctions: the multi-dimensional case. Discrete and continuous dynamical systems – series A, Vol. 37, no. 12, p. 6405 – 6435. doi | hal | arxiv | pdf
  • Avec R. Monneau. Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks.Annales Scientifiques de l’ÉNS, 50, fascicule 2, pp. 357-448hal | arXiv | pdf

2016

  • Avec R. Shvydkoy et F. Vigneron. Global well-posedness for a non-local Burgers’s equation: the periodic case. Annales de la faculté des sciences de Toulouse, Sér. 6, 25 no. 4 (2016), p. 723-758doi | hal | arxiv | pdf
  • Avec L. Silvestre. Estimates on elliptic equations that hold only where the gradient is large. Journal of the European Mathematical Society, Vol 18, pp. 1321–1338.doi | hal | arXiv | pdf
  • Finite speed of propagation for a non-local porous medium equation. Colloquium Mathematicum, Vol.143, No. 2, pp. 149-157doi | hal | arxiv

2015

  • Avec G. Galise et R. Monneau. A junction condition by specified homogenization and application to traffic lights Analysis and PDE, Vol 8, No 8, 1891–1929doi | hal | arxiv | pdf
  • Avec A. Mellet. Self-similar solutions for a fractional thin film equation governing hydraulic fractures. Communications in Mathematical Physics, vol 340, no. 3, 1187–1229 doi | hal | arxiv | pdf
  • Avec N. Forcadel et R. Monneau. Steady state and long time convergence of spirals moving by forced mean curvature motion. Communications in Partial Differential Equations, 40:6, 1137-1181. doi | hal | arxiv | pdf
  • Avec P. Biler and G. Karch. Nonlocal porous medium equation: Barenblatt profiles and other weak solutions. Archive for Rational Mechanics and Analysis (2015), Vol 215, No 2, pp. 497–529doi | hal | arxiv | pdf

2014

  • Avec G. Barles, E. Chasseigne et A. Ciomaga. Large Time Behavior of Periodic Viscosity Solutions for Uniformly Elliptic Integro-Differential Equations. Calculus of Variations and Partial Differential Equations, 50, no. 1-2, pp. 283–304.doi | hal | arxiv | pdf

2013

  • Avec R. Monneau et H. Zidani. A Hamilton-Jacobi approach to junction problems and application to traffic flows. ESAIM: Control, Optim. and Calc. Var. (2013), Vol 19, No 1, pp. 129-166.doi | hal | arxiv | pdf
  • Avec L. Silvestre. C1,α regularity of solutions of degenerate fully non-linear elliptic equations. Advances in Mathematics, Vol 233, pp. 196–206 doi | hal | arxiv | pdf

2012

  • Avec A. Mellet. Electrified thin films: Global existence of non-negative solutions. Annales de l’IHP, analyse non-linéaire (2012), Vol 29, No 11, 413–433doi | hal | arxiv | pdf
  • Avec G. Barles, E. Chasseigne et A. Ciomaga. Lipschitz regularity of solutions for mixed integro-differential equations. Journal of Differential Equations Vol 252 (2012), 6012–6060doi | hal | arxiv | pdf
  • Avec N. Forcadel et R. Monneau. Uniqueness and existence of spirals moving by forced mean curvature motion. Interfaces and Free Boundaries (2012), Vol 14, pp. 365–400doi | hal | arxiv | pdf
  • Avec N. Forcadel et R. Monneau. Homogenization of accelerated Frenkel-Kontorova models with n types of particles. Trans. Am. Math. Soc. 364 (2012) 6187-6227. doi | hal | arxiv | pdf

2011

  • Avec A. Mellet. Existence of solutions for a higher order non-local equation appearing in crack dynamics. Nonlinearity 24 (2011) 3487–3514doi | hal | arxiv | pdf
  • 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) doi | hal | arxiv | pdf
  • Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations. Journal of Differential Equations Vol 250, Issue 3 (2011), 1325–1766doi | hal | arxiv | pdfThe proof of the Harnack inequality (Corollary 1) contained in this paper is not correct. A correct one is given here.
  • Avec S. Serfaty. Repeated games for eikonal equations, integral curvature flows and integro-differential parabolic equations. Discrete Contin. Dyn. Syst. 29, 4 (2011), 1517–1552doi | hal | arxiv | pdf

2010

  • Avec B. Bouchard et R. Elie. Optimal control under stochastic target constraints. SIAM J. Control Optim. Volume 48, Issue 5, pp. 3501-3531 (2010)hal | pdf
  • 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)doi | hal | arxiv | pdf

2009

  • 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, 785-826hal | pdf
  • Level set approach for fractional mean curvature flows. Interfaces and Free Boundaries (2009), Vol 11, Issue 1, 153-176doi | hal | arxiv | pdf
  • Avec N. Forcadel et R. Monneau. Homogenization of the fully overdamped Frenkel-Kontorova models. J. Differential Equations 246 (2009), 1057-1097doi | hal | pdf
  • Avec N. Alibaud. Fractional semi-linear parabolic equations with unbounded data. Transations of the American Mathematical Society 361 (2009), 2527-2566doi | hal | pdf

2008

  • 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 — 516doi | hal | pdf
  • Avec G. Barles. Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions’ Theory Revisited. Annales de l’IHP (2008), Volume 25, No 3, Pages 567-585doi | hal | arxiv | pdf
  • 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), 49-89doi | hal | pdf
  • 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, 213-146doi | hal | pdf
  • Avec I. Gentil. The Lévy-Fokker-Planck equation: Φ-entropies and convergence to equilibrium. Asymptotic Analysis (2008), Vol 59, No 3-4, 125-138doi | hal | pdf

2001-2006

  • Convexity of solutions and C1,1 estimates for fully nonlinear elliptic equations. Journal de Mathématiques Pures et Appliquées, Vol 85, Issue 6 (2006), pp. 791-807 doi | hal | pdf
  • Avec J. Droniou. Fractal first order partial differential equations. Archive for Rational Mechanics and Analysis, Vol 182, No 2 (2006), pp. 299-331doi | hal | pdf
  • A non-local regularization of first order Hamilton-Jacobi equations. Journal of Differential Equations, Vol 211, Issue 1 (2005), pp. 218-246doi | hal | pdf
  • 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. 214-232doi | hal | pdf
  • 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. 689-714doi | hal | pdf
  • Support functions of Clarke’s generalized jacobian and of its plenary hull. Nonlinear Analysis, Theory, Methods and Applications, Vol 29, No 8 (2002) pp. 1111-1125hal | pdf
  • Some regularity results for anisotropic motion of fronts. Differential and Integral Equations, Vol 15, No 10 (2002) pp. 1263-1271hal | pdf
  • Avec Michel Volle. On vectorial Hamiton-Jacobi equations. Control and Cybernetics, Vol 31, No 3 (2002) pp. 493-506 hal | pdf
  • Convex Analysis techniques for Hopf-Lax formulae in Hamilton-Jacobi equations. Journal of Nonlinear and Convex Analysis Vol 2, No 3 (2001) pp. 333-343hal | pdf

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. 1275-1278hal | pdf
  • 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, 401-414doi | arxiv | pdf
  • 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.doi | hal | arxiv | pdf

Notes non publiées

  • Avec M. Koumaiha. Error estimates for finite difference schemes associated with Hamilton-Jacobi equations on a junction.hal | arxiv
  • Avec T. Souganidis. Phasefield theory for fractional diffusion-reaction equations and applications.hal | arxiv
  • Avec C. Mouhot. Hölder regularity for solutions to hypoelliptic equations with bounded measurable coefficients.hal | arxiv