Uniqueness results for a Dirichlet problem with variable exponent

V. V. Motreanu

doi:10.3934/cpaa.2010.9.1399

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2010, Volume 9, Issue 5: 1399-1410. Doi: 10.3934/cpaa.2010.9.1399

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Uniqueness results for a Dirichlet problem with variable exponent

V. V. Motreanu^1,

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

Received: August 31, 2009

Revised: August 31, 2009

Published: August 2010

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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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Mathematics Subject Classification: Primary: 35J60, 35J70; Secondary: 35D30.

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