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Uniqueness results for equations of the p(x)-Laplacian type


Antontsev, S; Chipot, M; Xie, Y (2007). Uniqueness results for equations of the p(x)-Laplacian type. Advances in Mathematical Sciences and Applications, 17(1):287-304.

Abstract

We study uniqueness of weak solutions of elliptic equations of the type
- div (a(x,u,∇u))+b(x,u)=f(x)
in a bounded domain Ω⊂ℝ n with Lipschitz boundary γ=∂Ω. We consider in particular mixed boundary conditions - i.e. Dirichlet condition on one part of the boundary and Neumann condition on the other part. A model equation could be
- div (a(x,u)|∇u|p(x)-2∇u)+b(x,u)=f(x),x∈Ω·
We establish uniqueness results for these equations. We also indicate conditions which guarantee existence of solution.

Abstract

We study uniqueness of weak solutions of elliptic equations of the type
- div (a(x,u,∇u))+b(x,u)=f(x)
in a bounded domain Ω⊂ℝ n with Lipschitz boundary γ=∂Ω. We consider in particular mixed boundary conditions - i.e. Dirichlet condition on one part of the boundary and Neumann condition on the other part. A model equation could be
- div (a(x,u)|∇u|p(x)-2∇u)+b(x,u)=f(x),x∈Ω·
We establish uniqueness results for these equations. We also indicate conditions which guarantee existence of solution.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2007
Deposited On:11 Nov 2009 15:35
Last Modified:05 Apr 2016 13:23
Publisher:Gakko Tosho
ISSN:1343-4373
Official URL:http://www1.gifu-u.ac.jp/~aiki/AMSA/vol17.html
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2337380

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