Calculus of Variations and Geometric Measure Theory

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
modified on 14 Jun 2023


Published Paper

Inserted: 27 feb 2021
Last Updated: 14 jun 2023

Journal: Journal of Functional Analysis
Year: 2021
Doi: 10.13140/RG.2.2.19953.40807


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