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2011 Well-Posedness Result For a Nonlinear Elliptic Problem Involving Variable Exponent and Robin Type Boundary Condition
S. Ouaro, A. Tchousso
Afr. Diaspora J. Math. (N.S.) 11(2): 36-64 (2011).

Abstract

In this work we study the following nonlinear elliptic boundary value problem, $b(u)-div \; a(x,\nabla u)=f \hbox{ in }\Omega$, $a(x,\nabla u).\eta=-\left|u\right|^{p(x)-2}u \hbox{ on }\partial \Omega$, where $\Omega$ is a smooth bounded open domain in $\mathbb{R}^{N}$, $N \geq 1$ with smooth boundary $\partial\Omega$. We prove the existence and uniqueness of a weak solution for $f \in L^{\infty}(\Omega)$, the existence and uniqueness of an entropy solution for $L^{1}$-data $f$. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.

Citation

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S. Ouaro. A. Tchousso. "Well-Posedness Result For a Nonlinear Elliptic Problem Involving Variable Exponent and Robin Type Boundary Condition." Afr. Diaspora J. Math. (N.S.) 11 (2) 36 - 64, 2011.

Information

Published: 2011
First available in Project Euclid: 6 December 2011

zbMATH: 1242.35110
MathSciNet: MR2862564

Subjects:
Primary: 35J20
Secondary: 35B38, 35D30, 35J60

Rights: Copyright © 2011 Mathematical Research Publishers

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Vol.11 • No. 2 • 2011
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