Weighted Hardy-Sobolev type inequalities with boundary terms

TL;DR

This paper introduces a new class of weighted Hardy-Sobolev inequalities with boundary terms, which are crucial for analyzing elliptic problems with boundary conditions in unbounded domains.

Contribution

It establishes novel weighted Hardy-Sobolev inequalities under mild assumptions, extending the tools available for boundary value problems in unbounded domains.

Findings

Derived new weighted Hardy-Sobolev inequalities.

Established corresponding weighted Sobolev and trace inequalities.

Enhanced analysis capabilities for elliptic problems with boundary conditions.

Abstract

In this paper we establish a new class of weighted Hardy-Sobolev type inequalities under mild monotonicity assumptions on the weight function. As a consequence, we derive the corresponding weighted Sobolev and trace-type inequalities. These results play an important role in the analysis of elliptic problems with Neumann or Robin boundary conditions in unbounded domains.