Finsler Hardy inequalities

TL;DR

This paper introduces a unified approach to anisotropic Hardy inequalities involving Finsler distances, establishing sharp constants and their non-attainability across different settings.

Contribution

It provides a novel, simplified method for deriving Finsler Hardy inequalities with proofs of sharpness and non-attainability of constants.

Findings

Established sharp Finsler Hardy inequalities in various contexts.

Proved the non-attainability of the optimal constants.

Presented a unified approach simplifying previous methods.

Abstract

In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a point or from the boundary of a domain. The sharpness and the non-attainability of the constants in the inequalities are also proved.