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# Uniqueness results for a Dirichlet problem with variable exponent

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

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