2021
DOI: 10.48550/arxiv.2108.09514
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Poincaré Inequalities and Neumann Problems for the Variable Exponent Setting

Abstract: We extend the results of [5], where we proved an equivalence between weighted Poincaré inequalities and the existence of weak solutions to a family of Neumann problems related to a degenerate p-Laplacian. Here we prove a similar equivalence between Poincaré inequalities in variable exponent spaces and solutions to a degenerate p(•)-Laplacian, a non-linear elliptic equation with nonstandard growth conditions.

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