69 citations · 106 across the 18 of their papers we have counts for
3 papers · 2 filters
Fully nonlinear integro-differential equations with deforming kernels
Luis Caffarelli, Rafayel Teymurazyan, José Miguel Urbano
We develop a regularity theory for integro-differential equations with kernels deforming in space like sections of a convex solution of a Monge-Ampère equation. We prove an ABP est…
Existence of weak solutions to a continuity equation with space time nonlocal Darcy law
Luis Caffarelli, Maria Gualdani, Nicola Zamponi
In this manuscript we consider a porous medium equation with non-local diffusion effects given by a fractional heat operator in two space dimensions. Global i…
[Regularity of interfaces for a Pucci type segregation problem
Luis Caffarelli, Stefania Patrizi, Veronica Quitalo +1
We show the existence of a Lipschitz viscosity solution in to a system of fully nonlinear equations involving Pucci-type operators. We study the regularity of the interface…