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> <p><i>F</i>(D2u,x) = ƒ(x) x ∈ Ω,</p> <p>u(x) = g(x) x ∈ ∂Ω</p> <p>has a solution u in C2(Ω) ∩ <i>C</i>(Ώ), and</p> <p><i>F</i>(<i>D</i>2v(x),x) = ƒ(x) x ∈ Ω\<i>S</i>,</p> <p>v(x) = g(x) x ∈ ∂Ω</p> <p>has a solution v in <i>C</i>2(Ω\<i>S</i>)∩Lip(Ω)∩<i>C</i>(Ώ). We prove that under certain conditions on <i>S</i> and v, the singular set <i>S</i> is removable; i.e., u = v.