Removable Singular Sets of Fully Nonlinear Elliptic Equations

Abstract

In this paper we consider fully nonlinear elliptic equations, including the Monge-Ampere equation and the Weingarden equation. We assume that F(D2u,x) = ƒ(x) x ∈ Ω, u(x) = g(x) x ∈ ∂Ω has a solution u in C2(Ω) ∩ C(Ω¯), and F(D2v(x), x) = ƒ(x) x ∈ Ω\S v(x) = g(x) x ∈ ∂Ω has a solution v in C2(Ω\S) ∩ Lip (Ω) ∩ C (Ω¯). We prove that under certain conditions on S and v, the singular set S is removable; i.e., u = v.