2.3k citations · 4.2k across the 53 of their papers we have counts for
66 papers
Interaction of a free boundary with a diffusion on a plane: analogy with the obstacle problem
Luis A. Caffarelli, Jean-Michel Roquejoffre, Ignacio Tomasetti
A horizontal -dimensional plane, having a diffusion of its own, exchanges with the lower half space. There, a reaction-diffusion process, modelled by a free boundary problem, ta…
The Two-Phase Stefan Problem with Anomalous Diffusion
Ioannis Athanasopoulos, Luis Caffarelli, Emmanouil Milakis
The non-local in space two-phase Stefan problem (a prototype in phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admi…
On a family of fully nonlinear integro-differential operators: From fractional Laplacian to nonlocal Monge-Ampère
Luis A. Caffarelli, María Soria-Carro
We introduce a new family of intermediate operators between the fractional Laplacian and the Caffarelli-Silvestre nonlocal Monge-Ampère that are given by infimums of integro-differ…
Fully Nonlinear Equations with Applications to Grad Equations in Plasma Physics
Luis Caffarelli, Ignacio Tomasetti
In this paper we generalize an equation studied by Mossino and Temam, to the fully nonlinear case. This equation arises in plasma physics as an approximation to Grad equations, whi…
Regularity for interface transmission problems
L. A. Caffarelli, M. Soria-Carro, P. R. Stinga
We study existence, uniqueness, and optimal regularity of solutions to transmission problems for harmonic functions with interfaces. For this, we develop a novel geometri…
The shape of a free boundary driven by a line of fast diffusion
Luis Caffarelli, Jean-Michel Roquejoffre
We complete the description, initiated in [6], of a free boundary travelling at constant speed in a half plane, where the propagation is controlled by a line having a large diffusi…