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Uniqueness results for a Dirichlet problem with variable exponent


Motreanu, V V (2010). Uniqueness results for a Dirichlet problem with variable exponent. Communications on Pure and Applied Analysis, 9(5):1399-1410.

Abstract

We study the uniqueness of weak solutions for Dirichlet problems with variable exponent and non-standard growth conditions. First, we provide two uniqueness results under ellipticity type hypotheses. Next, we provide a uniqueness result when the operator driving the problem is in the form of the divergence of a monotone map. Finally, we derive a fourth uniqueness result under homogeneity type hypotheses, by means of a comparison result and approximation.

Abstract

We study the uniqueness of weak solutions for Dirichlet problems with variable exponent and non-standard growth conditions. First, we provide two uniqueness results under ellipticity type hypotheses. Next, we provide a uniqueness result when the operator driving the problem is in the form of the divergence of a monotone map. Finally, we derive a fourth uniqueness result under homogeneity type hypotheses, by means of a comparison result and approximation.

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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:September 2010
Deposited On:15 Nov 2010 11:50
Last Modified:05 Apr 2016 14:16
Publisher:American Institute of Mathematical Sciences
ISSN:1534-0392
Publisher DOI:https://doi.org/10.3934/cpaa.2010.9.1399

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