Nonlocal geometric expansion of convex Planar Curves

Abstract

We consider a class of nonlocal geometric equations for expanding curves in the plane, arising in the study of evolutions governed by Monge-Kantorovich mass transfer. We construct convex solutions, given convex initial data. In order to obtain such solutions, we develop a new version of Perron's method. We give applications to the problem of characterizing fast/slow diffusion limits.