Uniqueness results for a Dirichlet problem with variable exponent

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September 2010, 9(5): 1399-1410. doi: 10.3934/cpaa.2010.9.1399

Uniqueness results for a Dirichlet problem with variable exponent

1.	Universität Zürich, Institut für Mathematik, CH-8057 Zürich, Switzerland

Received September 2009 Revised September 2009 Published May 2010

Abstract
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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.

Keywords: subsolution, uniqueness of weak solution, p(x)-Laplacian equation, approximation., supersolution, Variable exponent Dirichlet problem.

Mathematics Subject Classification: Primary: 35J60, 35J70; Secondary: 35D3.

Citation: V. V. Motreanu. Uniqueness results for a Dirichlet problem with variable exponent. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1399-1410. doi: 10.3934/cpaa.2010.9.1399

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