Uniqueness results for a Dirichlet problem with variable exponent
V. V. Motreanu - Universität Zürich, Institut für Mathematik, CH-8057 Zürich, Switzerland (email)
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.
Keywords: Variable exponent Dirichlet problem, p(x)-Laplacian equation, uniqueness
of weak solution, subsolution, supersolution, approximation.
Received: September 2009; Revised: September 2009; Published: May 2010.
2011 Impact Factor.692