Generalized weighted Hardy's inequalities with compact perturbations

TL;DR

This paper investigates a variational problem involving weighted Hardy inequalities with sharp missing terms, focusing on non-doubling weights related to boundary distance in bounded domains.

Contribution

It introduces a generalized framework for weighted Hardy inequalities with compact perturbations and analyzes cases with non-doubling weights.

Findings

Establishes new inequalities with sharp missing terms.

Extends Hardy inequalities to non-doubling weight functions.

Provides variational characterizations for these inequalities.

Abstract

In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights we treat non-doubling functions of the distance to the boundary of bounded domain.