Hardy's inequality for functions vanishing on a part of the boundary

TL;DR

This paper introduces a geometric framework for Hardy's inequality applicable to bounded domains where functions vanish only on part of the boundary, expanding the inequality's applicability.

Contribution

It presents a novel geometric approach to Hardy's inequality for functions vanishing on a subset of the boundary of a domain.

Findings

Established Hardy's inequality under new boundary conditions

Extended the inequality to more general boundary subsets

Provided geometric criteria for the inequality's validity

Abstract

We develop a geometric framework for Hardy's inequality on a bounded domain when the functions do vanish only on a closed portion of the boundary.