Uniqueness results for a Dirichlet problem with variable exponent
Viorica Venera Motreanu · Communications on Pure & Applied Analysis · 2010
We study the uniqueness of weak solutions for Dirichlet problemswith variable exponent and non-standard growth conditions. First, we providetwo uniqueness results under ellipticity type hypotheses. Next, we providea uniqueness result when the operator driving the problem is in the form ofthe divergence of a monotone map. Finally, we derive a fourth uniquenessresult under homogeneity type hypotheses, by means of a comparison resultand approximation.