Geodesic
Removeable singular sets of fully nonlinear elliptic equations
Electronic Journal of Differential Equations, Tome 1999 (1999).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Wang, Lihe and Zhu, Ning},
     title = {Removeable singular sets of fully nonlinear elliptic equations},
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     volume = {1999},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a0/}
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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__a0/