Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 04, pp. 1-5.
Title: Removable singular sets of fully nonlinear elliptic equations
Authors: Lihe Wang (Univ. of Iowa, USA)
Ning Zhu (Suzhou Univ., China)
Abstract:
In this paper we consider fully nonlinear elliptic equations,
including the Monge-Ampere equation and the Weingarden equation.
We assume that
$F(D^2u, x) = f(x) \quad x \in \Omega\,,$
$u(x) = g(x) \quad x\in \partial \Omega $
has a solution $u$ in $C^2(\Omega) \cap C(\bar {\Omega} )$, and
$F(D^2v(x), x) = f(x) \quad x\in \Omega\setminus S\,,$
$v(x)= g(x)\quad x\in \partial \Omega $
has a solution $v$ in
$C^2(\Omega\setminus S ) \cap \mbox{Lip}(\Omega) \cap C(\bar {\Omega})$.
We prove that under certain conditions on $S$ and $v$,
the singular set $S$ is removable; i.e., $u=v$.
Submitted March 17, 1998. Published February 17, 1999.
Math Subject Classification: 35B65
Key Words: Nonlinear PDE; Monge-Ampere Equation; Removable singularity.