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
Degenerate/Singular Equations (p-Laplacian type)
Nonlocal and Integro-Differential Equations
Harmonic Analysis
You can find all my papers and preprints on arXiv.
Publications and preprints
An elliptic-parabolic free boundary problem with discontinuous data
w/ Dennis Kriventsov, arXiv:2508.13299 (2025).
Fully nonlinear parabolic fixed transmission problems
w/ David Jesus, arXiv:2507.19277 (2025).
A parabolic free transmission problem: flat free boundaries are smooth
w/ Dennis Kriventsov, arXiv:2402.16805 (2024).
Transmission problems for simply connected domains in the complex plane
w/ María J. Carro and Virginia Naibo, Journal of Differential Equations (2024).
Lipschitz regularity for Poisson equations involving measures supported on C^{1,Dini} interfaces
w/ Iñigo U. Erneta, Communications in Partial Differential Equations (2024).
On a family of fully nonlinear integro-differential operators: From fractional Laplacian to nonlocal Monge-Ampère
w/ Luis A. Caffarelli, Analysis & PDE (2024).
Rellich identities for the Hilbert transform
w/ María J. Carro and Virginia Naibo, Journal of Functional Analysis (2024).
Regularity of viscosity solutions to fully nonlinear elliptic transmission problems
w/ Pablo R. Stinga, Advances in Mathematics (2023).
Regularity for C^{1,α} interface transmission problems
w/ Luis A. Caffarelli and Pablo R. Stinga, Archive for Rational Mechanics and Analysis (2021).
Other
Luis Caffarelli, premio Abel 2023: matemáticas y experiencias con sus colaboradores españoles [pdf]
La Gaceta de la RSME (2024)
El teorema de Müntz-Szász sobre la aproximación de funciones continuas [pdf]
w/ Daniel Eceizabarrena, Alejandro Mas-Mas, and Francisco Mengual-Bretón, TEMat (2017)