Geodesic
Removeable singular sets of fully nonlinear elliptic equations
Electronic journal of differential equations, Tome 1999 (1999)
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.
Classification : 35B65
Keywords: nonlinear PDE, Monge-Ampère equation, removable singularity 
@article{EJDE_1999__1999__a49,
     author = {Wang,  Lihe and Zhu,  Ning},
     title = {Removeable singular sets of fully nonlinear elliptic equations},
     journal = {Electronic journal of differential equations},
     year = {1999},
     volume = {1999},
     zbl = {0919.35027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a49/}
}
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AU  - Wang,  Lihe
AU  - Zhu,  Ning
TI  - Removeable singular sets of fully nonlinear elliptic equations
JO  - Electronic journal of differential equations
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VL  - 1999
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%A Wang,  Lihe
%A Zhu,  Ning
%T Removeable singular sets of fully nonlinear elliptic equations
%J Electronic journal of differential equations
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%F EJDE_1999__1999__a49
Wang,  Lihe; Zhu,  Ning. Removeable singular sets of fully nonlinear elliptic equations. Electronic journal of differential equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a49/