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 and preprints 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)