Publications

Lecture notes

De Giorgi’s regularity theory for elliptic, parabolic and kinetic equations. Univ. Berkeley Chancellor’s professor Lecture notes, fall 2025. hal | arxiv | doi

Preprints

With J. Guerand and C. Mouhot. Gehring’s Lemma for kinetic Fokker-Planck equations. hal | arxiv | doi
With N. Forcadel and R. Monneau. Germs for scalar conservation laws: the Hamilton-Jacobi equation point of view. hal | arxiv | doi
With P. Auscher and L. Niebel. Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness. hal | arxiv | doi
With F. Golse and L. Silvestre. Partial regularity in time for the space-homogeneous Boltzmann equation with very soft potentials. hal | arxiv | doi
With A. Loher. Conditional appearance of decay for the non-cutoff Boltzmann equation in a bounded domain. Annales de l’IHP, analyse non-linéaire (to appear). hal | arxiv | doi

Articles

With L. Silvestre and C. Villani. On the monotonicity of the Fisher information for the Boltzmann equation. Inventiones Mathematicae, 243, 127–179 (2026). hal | arxiv | doi
With P. Auscher and L. Niebel. Fundamental solutions to Kolmogorov-Fokker-Planck equations with rough coefficients: existence, uniqueness, upper estimates. SIAM J. Math. Anal. 57 (2), 2114–2137 (2025). hal | arxiv | doi
With N. Forcadel and R. Monneau. The twin blow-up method for Hamilton-Jacobi equations in higher dimension. ESAIM: COCV 31, 12 (2025). hal | arxiv | doi
With N. Forcadel and R. Monneau. Non-convex coercive Hamilton-Jacobi equations: Guerand’s relaxation revisited. Pure and Applied Analysis 6(4), 1055–1089 (2024). hal | arxiv | doi
With N. Forcadel and R. Monneau. Coercive Hamilton-Jacobi equations in domains: the twin blow-ups method. Comptes rendus. Mathématique 362, 829–839 (2024). hal | arxiv | doi
With F. Golse, S. Ji and A. F. Vasseur. Local regularity for the space homogeneous Landau equation with very soft potentials. Journal of Evolution Equations 24, article 82 (2024). hal | arxiv | doi
With J. Guerand. Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations. J. Inst. Math. Jussieu 22(6), 2749–2774 (2023). hal | arxiv | doi
With F. Golse, M. P. Gualdani and A. F. Vasseur. Partial Regularity in Time for the Space Homogeneous Landau Equation with Coulomb Potential. Ann. Sci. ENS 55(6), 1575–1611 (2022). hal | arxiv | doi
With L. Silvestre. Global regularity estimates for the Boltzmann equation without cut-off. JAMS 35(3), 625–703 (2022). hal | arxiv | doi
With L. Silvestre. The Schauder estimate for kinetic integral equations. Analysis & PDE 14(1), 171–204 (2021). hal | arxiv | doi
With C. Mouhot. The Schauder estimate in kinetic theory with application to a toy nonlinear model. Annales Henri Lebesgue 4, 369–405 (2021). hal | arxiv | doi
With L. Silvestre. Regularity for the Boltzmann equation conditional to macroscopic bounds. EMS Surveys in Mathematical Sciences 7, 117–172 (2020). hal | arxiv | doi
With R. Tarhini and F. Vigneron. Regularity of solutions of a fractional porous medium equation. Interfaces and Free Boundaries 22(4) (2020). hal | arxiv | doi
With C. Mouhot and L. Silvestre. Gaussian lower bounds for the Boltzmann equation without cut-off. SIAM J. Math. Anal. 52(3), 2930–2944 (2020). hal | arxiv | doi
With L. Silvestre. The weak Harnack inequality for the Boltzmann equation without cut-off. JEMS 22(2), 507–592 (2020). hal | arxiv | doi
With C. Mouhot and L. Silvestre. Decay estimates for large velocities in the Boltzmann equation without cut-off. J. École Polytechnique Math. 7, 143–184 (2020). hal | arxiv | doi
With T. Jin and L. Silvestre. Hölder gradient estimates for a class of singular or degenerate parabolic equations. Advances in Nonlinear Analysis 8(1), 845–867 (2019). hal | arxiv | doi
With F. Golse, C. Mouhot and A. F. Vasseur. Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation. Annali SNS Pisa XIX(1), 253–295 (2019). hal | arxiv | doi
With G. Barles, A. Briani and E. Chasseigne. Flux-limited and classical viscosity solutions for regional control problems. ESAIM: COCV 24, 1881–1906 (2018). hal | arxiv | doi
With T. Jin and R. Shvydkoy. Schauder estimates for an integro-differential equation with applications to a nonlocal Burgers equation. Ann. Fac. Sci. Toulouse 27(4), 667–677 (2018). hal | arxiv | doi
With V. D. Nguyen. Generalized junction conditions for degenerate parabolic equations. Calc. Var. PDE 56:157 (2017). hal | arxiv | doi
With R. Monneau. Quasi-convex Hamilton-Jacobi equations posed on junctions: the multi-dimensional case. DCDS-A 37(12), 6405–6435 (2017). hal | arxiv | doi
With R. Monneau. Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks. Ann. Sci. ENS 50(2), 357–448 (2017). hal | arxiv | doi
With R. Shvydkoy and F. Vigneron. Global well-posedness for a non-local Burgers’s equation: the periodic case. Ann. Fac. Sci. Toulouse 25(4), 723–758 (2016). hal | arxiv | doi
With L. Silvestre. Estimates on elliptic equations that hold only where the gradient is large. JEMS 18, 1321–1338 (2016). hal | arxiv | doi
Finite speed of propagation for a non-local porous medium equation. Colloquium Mathematicum 143(2), 149–157 (2016). hal | arxiv | doi
With G. Galise and R. Monneau. A junction condition by specified homogenization and application to traffic lights. Analysis & PDE 8(8), 1891–1929 (2015). hal | arxiv | doi
With A. Mellet. Self-similar solutions for a fractional thin film equation governing hydraulic fractures. CMP 340(3), 1187–1229 (2015). hal | arxiv | doi
With N. Forcadel and R. Monneau. Steady state and long time convergence of spirals moving by forced mean curvature motion. CPDE 40(6), 1137–1181 (2015). hal | arxiv | doi
With P. Biler and G. Karch. Nonlocal porous medium equation: Barenblatt profiles and other weak solutions. ARMA 215(2), 497–529 (2015). hal | arxiv | doi
With G. Barles, E. Chasseigne and A. Ciomaga. Large Time Behavior of Periodic Viscosity Solutions for Uniformly Elliptic Integro-Differential Equations. Calc. Var. PDE 50, 283–304 (2014). hal | arxiv | doi
With R. Monneau and H. Zidani. A Hamilton-Jacobi approach to junction problems and application to traffic flows. ESAIM: COCV 19(1), 129–166 (2013). hal | arxiv | doi
With L. Silvestre. C¹,α regularity of solutions of degenerate fully non-linear elliptic equations. Advances in Mathematics 233, 196–206 (2013). hal | arxiv | doi
With A. Mellet. Electrified thin films: Global existence of non-negative solutions. Ann. IHP Analyse non-linéaire 29, 413–433 (2012). hal | arxiv | doi
With G. Barles, E. Chasseigne and A. Ciomaga. Lipschitz regularity of solutions for mixed integro-differential equations. JDE 252, 6012–6060 (2012). hal | arxiv | doi
With N. Forcadel and R. Monneau. Uniqueness and existence of spirals moving by forced mean curvature motion. Interfaces Free Boundaries 14, 365–400 (2012). hal | arxiv | doi
With N. Forcadel and R. Monneau. Homogenization of accelerated Frenkel-Kontorova models with n types of particles. Trans. AMS 364, 6187–6227 (2012). hal | arxiv | doi
With A. Mellet. Existence of solutions for a higher order non-local equation appearing in crack dynamics. Nonlinearity 24, 3487–3514 (2011). hal | arxiv | doi
With G. Barles and E. Chasseigne. Hölder continuity of solutions of second-order elliptic integro-differential equations. JEMS 13(1), 1–26 (2011). hal | arxiv | doi
Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations. JDE 250(3) (2011). hal | arxiv | doi
With S. Serfaty. Repeated games for eikonal equations, integral curvature flows and integro-differential parabolic equations. DCDS 29(4), 1517–1552 (2011). hal | arxiv | doi
With B. Bouchard and R. Elie. Optimal control under stochastic target constraints. SIAM J. Control Optim. 48(5), 3501–3531 (2010). hal | arxiv | doi
With N. Alibaud and G. Karch. Asymptotic properties of entropy solutions to fractal Burgers equations. SIAM J. Math. Anal. 42(1), 354–376 (2010). hal | arxiv | doi
With N. Forcadel and R. Monneau. Homogenization of some particle systems with two-body interactions and of the dislocation dynamics. DCDS-A 23(3), 785–826 (2009). hal | arxiv | doi
Level set approach for fractional mean curvature flows. Interfaces Free Boundaries 11(1), 153–176 (2009). hal | arxiv | doi
With N. Forcadel and R. Monneau. Homogenization of the fully overdamped Frenkel-Kontorova models. JDE 246, 1057–1097 (2009). hal | arxiv | doi
With N. Alibaud. Fractional semi-linear parabolic equations with unbounded data. Trans. AMS 361, 2527–2566 (2009). hal | arxiv | doi
With R. Monneau and E. Rouy. Homogenization of first order equations with (u/ε)-periodic Hamiltonians. Part II: application to dislocation dynamics. CPDE 33(3), 479–516 (2008). hal | arxiv | doi
With G. Barles. Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions’ Theory Revisited. Ann. IHP 25(3), 567–585 (2008). hal | arxiv | doi
With R. Monneau. Homogenization of first order equations with (u/ε)-periodic Hamiltonians. Part I: local equations. ARMA 187, 49–89 (2008). hal | arxiv | doi
With G. Barles and E. Chasseigne. The Dirichlet problem for second-order elliptic integro-differential equations. Indiana Univ. Math. J. 57(1) (2008). hal | arxiv | doi
With I. Gentil. The Lévy-Fokker-Planck equation: Φ-entropies and convergence to equilibrium. Asymptotic Analysis 59(3-4), 125–138 (2008). hal | arxiv | doi
Convexity of solutions and C¹,¹ estimates for fully nonlinear elliptic equations. J. Math. Pures Appl. 85(6), 791–807 (2006). hal | arxiv | doi
With J. Droniou. Fractal first order partial differential equations. ARMA 182(2), 299–331 (2006). hal | arxiv | doi
A non-local regularization of first order Hamilton-Jacobi equations. JDE 211(1), 218–246 (2005). hal | arxiv | doi
With J. Vovelle. A kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications. SIAM Math. Anal. 36(1), 214–232 (2004). hal | arxiv | doi
With J. Droniou and J. Vovelle. An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions. Ann. IHP Analyse non linéaire 21(5), 689–714 (2004). hal | arxiv | doi
Support functions of Clarke’s generalized jacobian and of its plenary hull. Nonlinear Analysis 29(8), 1111–1125 (2002). hal | arxiv | doi
Some regularity results for anisotropic motion of fronts. Differential and Integral Equations 15(10), 1263–1271 (2002). hal | arxiv | doi
With M. Volle. On vectorial Hamilton-Jacobi equations. Control and Cybernetics 31(3), 493–506 (2002). hal | arxiv | doi
Convex Analysis techniques for Hopf-Lax formulae in Hamilton-Jacobi equations. Journal of Nonlinear and Convex Analysis 2(3), 333–343 (2001). hal | arxiv | doi

Notes and Proceedings

Fisher information for solutions of the Boltzmann equation. Short review, 14 p. hal | arxiv | doi
With F. Golse. Local regularity for the Landau equation (with Coulomb interaction potential). Kolmogorov operators and their applications (2024), 1–22. hal | arxiv | doi
With P. Biler and G. Karch. Barenblatt profiles for a nonlocal porous medium equation. C. R. Acad. Sci. Paris, Ser. I 349 (2011), 641–645. hal | arxiv | doi
With I. Gentil. Logarithmic Sobolev inequalities: regularizing effect of Lévy operators and asymptotic convergence in the Lévy-Fokker-Planck equation. hal | arxiv | doi
With J.-B. Hiriart-Urruty. Les fonctions d’appui de la jacobienne généralisée de Clarke et de son enveloppe plénière. C. R. Acad. Sci. Paris Sér. I Math. 326(11) (1998), 1275–1278. hal | arxiv | doi

Unpublished notes

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