Calculus of Variations and Geometric Measure Theory
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G. Di Fratta - A. Fiorenza

A unified divergent approach to Hardy-Poincaré inequalities in classical and variable Sobolev Spaces

created by difratta on 27 Feb 2021

[BibTeX]

Preprint

Inserted: 27 feb 2021
Last Updated: 27 feb 2021

Year: 2021
Doi: 10.13140/RG.2.2.19953.40807

Abstract:

We present a unified strategy to derive Hardy-Poincaré inequalities on bounded and unbounded domains. The approach allows proving a general Hardy-Poincaré inequality from which the classical Poincaré 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.

Keywords: Poincare inequality, Hardy inequality, Variable Sobolev Spaces


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