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May/June 2013 Uniqueness result for nonlinear anisotropic elliptic equations
Rosaria Di Nardo, Filomena Feo, Olivier Guibé
Adv. Differential Equations 18(5/6): 433-458 (May/June 2013).

Abstract

We consider here a class of anisotropic elliptic equations, in a bounded domain $\Omega$ with Lipschitz continuous boundary $\partial \Omega$, of the type $$ -\sum_{i=1}^{N}\partial_{x_{i}}\big(a_{i}(x,u) |\partial_{x_{i}}u|^{p_{i}-2}\partial_{x_{i}} u\big) =f- {\rm div} g $$ with Dirichlet boundary conditions. Using the framework of renormalized solutions we prove the uniqueness of the solution under a very local Lipschitz condition on the coefficients $a_{i}(x,s)$ with respect to $s$ and with $f$ belonging to $L^1(\Omega)$.

Citation

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Rosaria Di Nardo. Filomena Feo. Olivier Guibé. "Uniqueness result for nonlinear anisotropic elliptic equations." Adv. Differential Equations 18 (5/6) 433 - 458, May/June 2013.

Information

Published: May/June 2013
First available in Project Euclid: 14 March 2013

zbMATH: 1272.35092
MathSciNet: MR3086461

Subjects:
Primary: 35A02 , 35K20 , 35K55 , 35R05

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.18 • No. 5/6 • May/June 2013
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