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arXiv · 2103.06547

A unified divergent approach to Hardy-Poincar\'e inequalities in classical and variable Sobolev spaces

Giovanni Di Fratta·Alberto Fiorenza
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Abstract

We present a unified strategy to derive Hardy-Poincar\'e inequalities on bounded and unbounded domains. The approach allows proving a general Hardy-Poincar\'e inequality from which the classical Poincar\'e and Hardy inequalities immediately follow. The idea also applies to the more general context of variable exponent Sobolev spaces. The argument, concise and constructive, does not require a priori knowledge of compactness results and retrieves geometric information on the best constants.

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Giovanni Di Fratta, Alberto Fiorenza. 2021-03-11. A unified divergent approach to Hardy-Poincar\'e inequalities in classical and variable Sobolev spaces. https://doi.org/10.13140/rg.2.2.19953.40807

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