Removable Singular Sets of Fully Nonlinear Elliptic Equations

Abstract

<p>In this paper we consider fully nonlinear elliptic equations, including the Monge-Ampere equation and the Weingarden equation. We assume that</p> <pre>F(D²u,x) = ƒ(x) x ∈ Ω,<br> u(x) = g(x) x ∈ ∂Ω<br> has a solution u in C²(Ω) ∩ C(Ω¯), and<br> F(D²v(x), x) = ƒ(x) x ∈ Ω\S<br> v(x) = g(x) x ∈ ∂Ω</pre> <p>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.</p>