37 (2012), no. 9, 1668-1688. 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, 1169-1184. Joint work with Scott Armstrong and Charles Smart.
Holder continuity for a drift-diffusion equation with pressure
Annales de l'Institut Henri Poincare (C) Anal. Non Lineaire. 29 (2012), no. 4, 637-652. Joint work with Vlad Vicol.
Unique continuation for fully nonlinear elliptic equations
Mathematical Research Letters. Volume 18, Issue 5, September 2011 pp. 921-926. 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, 557-584.
On divergence free drifts.
Journal of Differential Equations 252 (2012), no. 1, 505-540. Joint work with Gregory Seregin, Vladimir Sverak and Andrej Zlatos.
Holder estimates for advection fractional-diffusion 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. 3-4, 301-321. Joint work with Huiqiang Jiang and Christopher Larsen.
Holder continuity for integro-differential parabolic equations with polynomial growth respect to the gradient
Discrete and Continuous Dynamical Systems Volume: 28, Number: 3, November 2010.
Eventual regularization of the slightly supercritical fractional Burgers equation.
A special issue Dedicated to Louis Nirenberg on the Occasion of his 85th Birthday Part II
Discrete and Continuous Dynamical Systems Volume: 27, Number: 2, June 2010.
On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion.
A special issue Trends and Developments in DE/Dynamics Part I
Joint work with Chi Hin Chan and Magdalena Czubak.
Advances in Mathematics. 226 (2011), no. 2, 2020-2039
Smooth approximations to solutions of nonconvex fully nonlinear elliptic equations.
American Mathematical Society Translations--Series 2 Advances in the Mathematical Sciences 2010; Volume: 229.
On the Evans-Krylov theorem.
Nonlinear Partial Differential Equations and Related Topics: Dedicated to Nina N. Uraltseva.
Joint work with Luis Caffarelli.
Proceedings of the AMS. 138 (2010), 263-265. Joint work with Luis Caffarelli.
The Evans-Krylov theorem for non local fully non linear equations.
Annals of Mathematics.174 (2011), no. 2, 1163-1187. 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 quasi-geostrophic equation
Annales de l'Institut Henri Poincare (C) Anal. Non Lineaire 27 (2010), Issue 2, Pages 693-704
The Dirichlet Problem for the Convex Envelope
Transactions of the AMS. 363 (2011), no. 11, 5871-5886. Joint work with Adam Oberman.
Regularity theory for fully nonlinear integro-differential equations.
Communications on Pure and Applied Mathematics. 62 (2009) Issue 5, 597--638. Joint work with L. Caffarelli.
A characterization of optimal two-phase multifunctional composite designs
Proc. R. Soc. A
Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
463, Number 2086 (2007). The source code of the numerical tests relevant to this paper can be downloaded here
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:
Regularity of the obstacle problem for a fractional power of the laplace operator.
Calculus of variations and nonlinear partial differential equations, 43--74, Lecture Notes in Math., 1927, Springer, Berlin, 2008.
Communications on Pure and Applied Mathematics.
Regularity for fully nonlinear elliptic equations with Neumann boundary data.
60 (2007), no. 1, 67--112.
This article is based on My PhD Thesis
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), 1155-1174.
The two membranes problem.
Communications in Partial Differential Equations 30 (2005), no. 1-3, 245--257
Weak matrix majorization.
Linear Algebra Appl. 403 (2005), 343--368. Joint work with Francisco Martínez Pería and Pedro Massey
The articles below will not be published but might be of interest to some people.
Partially supported by NSF.