Electron.n. J. Diff. Eqns., Vol. 1999(1999), No. 04, pp. 1-5.

Removable singular sets of fully nonlinear elliptic equations

Lihe Wang & Ning Zhu

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 $C^2(\Omega\setminus S ) \cap \hbox{Lip}(\Omega) \cap C(\bar {\Omega})$.
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.

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Lihe Wang
Department of Mathematics, University of Iowa
Iowa City, IA 52242, USA
e-mail: lwang@math.uiowa.edu

Ning Zhu
Department of Mathematics, Suzhou University
Suzhou 215006, China

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