DG-MP-PDE Seminar: Luis Silvestre

Abstract

We prove that solutions to a fully nonlinear elliptic equation F(D^2u)=0 are classical outside a set of dimension at most n-epsilon, where n is the dimension and epsilon is a small constant depending on the ellipticity bounds of F and dimension. We do not make any convexity assumption on the equation F, but we assume that it is differentiable. We will also discuss the relationship of the partial regularity result with the question of unique continuation of solutions. This is a joint work with Scott Armstrong and Charles Smart.