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1996 Singular boundary value problems for nonlinear elliptic equations in nonsmooth domains
Jean Fabbri, Laurent Veron
Adv. Differential Equations 1(6): 1075-1098 (1996).

Abstract

Let $\Omega$ be a piecewise-regular domain in $\Bbb R^N$ and O an irregular point on its boundary $\partial \Omega$. We study under what conditions on $q$ any solution $u$ of (E) $-\Delta u + g(x,u)=0$ where $g$ has a $q$-power-like growth at infinity ($q>1$) which coincides on $\partial \Omega \setminus {\{\text{O}}\}$ with a continuous function defined on whole $\partial \Omega$, can be extended as a continuous function in $\bar \Omega$.

Citation

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Jean Fabbri. Laurent Veron. "Singular boundary value problems for nonlinear elliptic equations in nonsmooth domains." Adv. Differential Equations 1 (6) 1075 - 1098, 1996.

Information

Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0863.35021
MathSciNet: MR1409900

Subjects:
Primary: 35J65
Secondary: 35B65

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.1 • No. 6 • 1996
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