
Decay estimates for large velocities in the Boltzmann equation without cutoff
Preprint. Joint work with Cyril Imbert and Clement Mouhot.
 Oscillation properties of scalar conservation laws.
Communications on Pure and Applied Mathematics. Accepted for publication.
 Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials.
Annales de l'Institut Henri Poincare (C) Anal. Non Lineaire. Accepted for publication. Joint work with Stephen Cameron and Stanley Snelson.
 The weak Harnack inequality for the Boltzmann equation without cutoff.
Journal of the European Mathematical Society. Accepted for publication. Joint work with Cyril Imbert.
 Hölder gradient estimates for a class of singular or degenerate parabolic equations.
Preprint. Joint work with Cyril Imbert and Tianling Jin.
 Upper bounds for parabolic equations and the Landau equation.
Journal of Differential Equations 262 (2017), no. 3, 3034–3055.
 An integrodifferential equation without continuous solutions.
Mathematical Research Letters 23 (2016), no. 4, 1157–1166. Joint work with Stanley Snelson.
 Hölder gradient estimates for parabolic homogeneous pLaplacian equations.
Journal de Mathématiques Pures et Appliquées. (9) 108 (2017), no. 1, 63–87. Joint work with Tianling Jin.
 Regularity estimates for fully non linear elliptic equations which are asymptotically convex.
Progress in Nonlinear Differential Equations and their Applications. Contributions to nonlinear elliptic equations and systems, 425–438, 86, Birkhäuser/Springer, Cham, 2015. Joint work with Eduardo Teixeira.
 A new regularization mechanism for the Boltzmann equation without cutoff.
Communications in Mathematical Physics 348 (2016), no. 1, 69–100.
 Regularity for parabolic integrodifferential equations with very irregular kernels.
Analysis and PDE 9 (2016), no. 3, 727–772. Joint work with Russell Schwab.
 Propagation in a non local reaction diffusion equation with spatial and genetic trait structure.
Nonlinearity 29 (2016), no. 4, 1434–1466. Joint work with Henri Berestycki and Tianling Jin.
 Regularity estimates for parabolic integro
differential equations and applications.
Proceedings of the ICM 2014.
 On a transport equation with nonlocal drift
Transactions of the AMS. 368 (2016), no. 9, 6159–6188. Joint work with Vlad Vicol. The article is about
this equation.
 A non local MongeAmpere equation.
Communications in Analysis and Geometry. 24 (2016), no. 2, 307–335. Joint work with Luis Caffarelli.
 On Landis' conjecture in the plane
Communications in Partial Differential Equations. 40 (2015), no. 4, 766–789. Joint work with Carlos Kenig and JennNan Wang.
 Overdetermined problems for fully nonlinear elliptic equations
Calculus of Variations and PDE. 54 (2015), no. 1, 989–1007. Joint work with Boyan Sirakov.
 Boundary regularity for viscosity solutions of fully nonlinear elliptic equations
Communications in Partial Differential Equations . 39 (2014), no. 9, 16941717. Joint work with Boyan Sirakov.
 Estimates on elliptic equations that hold only where the gradient is large
Journal of the European Mathematical Society. 18 (2016), no. 6, 1321–1338. Joint work with Cyril Imbert.
 Uniqueness of radial solutions for the fractional Laplacian
Communications on Pure and Applied Mathematics . 69 (2016), no. 9, 1671–1726. Joint work with Rupert Frank and Enno Lenzmann.
 Holder regularity for generalized master equations with rough kernels
Published as chapter 4 in the book Advances in Analysis: The Legacy of Elias M. Stein. Princeton University Press, 2014. Joint work with Luis Caffarelli.
 On the loss of continuity for supercritical driftdiffusion equations
Archive of Rational Mechanics and Analysis. 207 (2013), no. 3, 845877. Joint work with Vlad Vicol and Andrej Zlatos.
 Global wellposedness of slightly supercritical active scalar equations.
Analysis and PDE . 7 (2014), no. 1, 4372. Joint work with Michael Dabkowski, Alexander Kiselev and Vlad Vicol.
 $C^{1,\alpha}$ regularity of solutions of degenerate fully nonlinear elliptic equations.
Advances in Mathematics. 233 (2013), 196206. Joint work with Cyril Imbert.
 Holder continuity to HamiltonJacobi equations with superquadratic growth in the gradient and unbounded righthand side
Communications in Partial Differential Equations. 37 (2012), no. 9, 16681688. Joint work with Pierre Cardaliaguet.
 Partial regularity of solutions of fully nonlinear uniformly elliptic equations
Communications on Pure and Applied Mathematics 65 (2012), no.8, 11691184. Joint work with Scott Armstrong and Charles Smart.
 Holder continuity for a driftdiffusion equation with pressure
Annales de l'Institut Henri Poincare (C) Anal. Non Lineaire. 29 (2012), no. 4, 637652. Joint work with Vlad Vicol.
 Unique continuation for fully nonlinear elliptic equations
Mathematical Research Letters. Volume 18, Issue 5, September 2011 pp. 921926. Joint work with Scott Armstrong.
 On the differentiability of the solution to an equation with drift and fractional diffusion.
Indiana University Mathematical Journal. 61 (2012), no. 2, 557584.
 On divergence free drifts.
Journal of Differential Equations 252 (2012), no. 1, 505540. Joint work with Gregory Seregin, Vladimir Sverak and Andrej Zlatos.
 Holder estimates for advection fractionaldiffusion equations.
Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Accepted for publication.
 Full regularity of a free boundary problem with two phases.
Calculus of Variations and PDE 42 (2011), no. 34, 301321. Joint work with Huiqiang Jiang and Christopher Larsen.
 Holder continuity for integrodifferential parabolic equations with polynomial growth respect to the gradient
Discrete and Continuous Dynamical Systems Volume: 28, Number: 3, November 2010.
A special issue Dedicated to Louis Nirenberg on the Occasion of his 85th Birthday Part II
 Eventual regularization of the slightly supercritical fractional Burgers equation.
Discrete and Continuous Dynamical Systems Volume: 27, Number: 2, June 2010.
A special issue Trends and Developments in DE/Dynamics Part I
Joint work with Chi Hin Chan and Magdalena Czubak.
 On the differentiability of the solution to the HamiltonJacobi equation with critical fractional diffusion.
Advances in Mathematics. 226 (2011), no. 2, 20202039
 Smooth approximations to solutions of nonconvex fully nonlinear elliptic equations.
American Mathematical Society TranslationsSeries 2 Advances in the Mathematical Sciences 2010; Volume: 229.
Nonlinear Partial Differential Equations and Related Topics: Dedicated to Nina N. Uraltseva.
Joint work with Luis Caffarelli.
 On the EvansKrylov theorem.
Proceedings of the AMS. 138 (2010), 263265. Joint work with Luis Caffarelli.
 The EvansKrylov theorem for non local fully non linear equations.
Annals of Mathematics.174 (2011), no. 2, 11631187. Joint work with Luis Caffarelli.
 Regularity results for nonlocal equations by approximation
Archive of Rational Mechanics and Analysis. Volume 200, Issue 1 (2011), Page 59. Joint work with Luis Caffarelli.
 Eventual regularization for the slightly supercritical quasigeostrophic equation
Annales de l'Institut Henri Poincare (C) Anal. Non Lineaire 27 (2010), Issue 2, Pages 693704
 The Dirichlet Problem for the Convex Envelope
Transactions of the AMS. 363 (2011), no. 11, 58715886. Joint work with Adam Oberman.
 Regularity theory for fully nonlinear integrodifferential equations.
Communications on Pure and Applied Mathematics. 62 (2009) Issue 5, 597638. Joint work with L. Caffarelli.
 A characterization of optimal twophase multifunctional composite designs
Proc. R. Soc. A 463, Number 2086 (2007). The source code of the numerical tests relevant to this paper can be downloaded
here.
 Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
Inventiones Mathematicae. 171, Number 2 (2008). Joint work with Luis Caffarelli and Sandro Salsa.
 Regularity for the nonlinear Signorini problem
Advances in Mathematics. 217, Issue 3 (2008). Joint work with Manolis Milakis.
 An extension problem related to the fractional Laplacian
Communications in Partial Differential Equations, 32 (2007) Issue 8, 1245. Joint work with Luis Caffarelli.
 Issues in homogenization for problems with nondivergence structure.
Lecture notes of Luis Caffarelli's course in a CIME summer school. Published as a chapter of the book:
Calculus of variations and nonlinear partial differential equations, 4374, Lecture Notes in Math., 1927, Springer, Berlin, 2008.
 Regularity of the obstacle problem for a fractional power of the laplace operator.
Communications on Pure and Applied Mathematics. 60 (2007), no. 1, 67112.
This article is based on
My PhD Thesis
 Regularity for fully nonlinear elliptic equations with Neumann boundary data.
Communications in Partial Differential Equations 31 (2006), No. 8. Joint work with Manolis Milakis.
 Holder estimates for solutions of integro differential equations like the fractional Laplacian.
Indiana University Mathematical Journal 55 (2006), 11551174.
 The two membranes problem.
Communications in Partial Differential Equations 30 (2005), no. 13, 245257
 Weak matrix majorization.
Linear Algebra Appl. 403 (2005), 343368. Joint work with Francisco Martínez Pería and Pedro Massey
The articles below will not be published but might be of interest to some people.