Research

I work in regularity theory of elliptic and parabolic Partial Differential Equations. Some topics I am interested in are:

• Transmission and Free Boundary  Problems

• Fully Nonlinear Equations

• Nonlocal and Integro-Differential Equations

• Harmonic Analysis

You can find all my papers on arXiv.

Publications and preprints

• Lipschitz regularity for Poisson equations involving measures supported on C^{1,dini} interfaces, with I. U. Erneta, submitted, 2024.

• Transmission problems for simply connected domains in the complex plane, with M. J. Carro and V. Naibo, submitted, 2024.

• A parabolic free transmission problem: flat free boundaries are smooth, with D. Kriventsov, submitted, 2024.

• On a family of fully nonlinear integro-differential operators: From fractional Laplacian to nonlocal Monge-Ampère, with L. A. Caffarelli, Anal. PDE, 2024.

• Rellich identities for the Hilbert transform, with M. J. Carro and V. Naibo,  J. Funct. Anal., 2024.

• Regularity of viscosity solutions to fully nonlinear elliptic transmission problems, with P. R. Stinga, Adv. Math., 2023.

• Regularity for C^{1,α} interface transmission problems, with L. A. Caffarelli and P. R. Stinga, Arch. Ration. Mech. Anal, 2021.

Other

• Luis Caffarelli, premio Abel 2023: matemáticas y experiencias con sus colaboradores españoles, Gac. R. Soc. Mat. Esp., 2024 (pdf)

• El teorema de Müntz-Szász sobre la aproximación de funciones continuas, with D. Eceizabarrena, A. Mas-Mas, and F. Mengual-Bretón, TEMat, 2017 (pdf)