Hardy-Sobolev inequalities with distance to the boundary weight functions

TL;DR

This paper establishes sharp weighted Hardy-Sobolev inequalities with boundary-distance weights, advancing understanding of elliptic equations and functional inequalities in mathematical analysis.

Contribution

It introduces the first sharp Hardy-Sobolev inequalities involving boundary-distance weights, contributing novel results to the field of elliptic PDEs and functional analysis.

Findings

Proved new sharp weighted Hardy-Sobolev inequalities

Linked inequalities to elliptic equations

Provided foundational results for further research

Abstract

This is the first part of our research on certain sharp Hardy-Sobolev inequalities and the related elliptic equations. In this part we shall establish some sharp weighted Hardy-Sobolev inequalities whose weights are distance functions to the boundary.