Publications

Pré-publications

  • Avec P. Auscher et L. Niebel. Fundamental solutions to Kolmogorov-Fokker-Planck equations with rough coefficients: existence, uniqueness, upper estimates. hal | arxiv
  • Avec P. Auscher et L. Niebel. Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness. hal | arxiv
  • Avec N. Forcadel et R. Monneau. The twin blow-up method for Hamilton-Jacobi equations in higher dimension. hal | arxiv
  • Avec F. Golse et L. Silvestre. Partial regularity in time for the space-homogeneous Boltzmann equation with very soft potentials. hal | arxiv
  • Avec N. Forcadel et R. Monneau. Non-convex coercive Hamilton-Jacobi equations: Guerand’s relaxation revisited. hal | arxiv
  • Avec F. Golse et A. F. Vasseur. Local regularity for the space homogeneous Landau equation with very soft potentials. hal | arxiv

À paraître

  • Avec N. Forcadel et R. Monneau. Coercive Hamilton-Jacobi equations in domains: the twin blow-ups method. Comptes rendus. Mathématique (à paraître). hal | arxiv

2023

  • Avec J. Guerand. Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations. Journal de l’institut mathématique de Jussieu. Volume 22 , Issue 6 , November 2023 , pp. 2749 – 2774. hal | arxiv | doi

2022

  • 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, Fascicule 6, tome 55, pp. 1575-1611. hal | arxiv
  • 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 | doi

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