11 citations · 17 across the 5 of their papers we have counts for
5 papers
The Evans-Krylov theorem for non local fully non linear equations
Luis Caffarelli, Luis Silvestre
We prove an interior regularity result for solutions of a purely integro-differential Bellman equation. This regularity is enough for the solutions to be understood in the classica…
Nonlocal minimal surfaces
L. A. Caffarelli, J. -M. Roquejoffre, O. Savin
The de Giorgi theory for minimal surfaces consists in studying sets whose indicator function is a (local) minimum of the BV norm. In this paper we replace the BV norm by the …
Some remarks on singular solutions of nonlinear elliptic equations. I
Luis Caffarelli, YanYan Li, Louis Nirenberg
The paper concerns singular solutions of nonlinear elliptic equations.
The structure of the free boundary for lower dimensional obstacle problems
I. Athanasopoulos, L. A. Caffarelli, S. Salsa
We study the regularity of the "free surface" in boundary obstacle problems. We show that near a non-degenerate point the free boundary is a -dimensional surface i…
Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
L. Caffarelli, A. Vasseur
Motivated by the critical dissipative quasi-geostrophic equation, we prove that drift-diffusion equations with L^2 initial data and minimal assumptions on the drift are locally Hol…