Sharp fractional Hardy inequalities in half-spaces

TL;DR

This paper establishes the exact constant in fractional Hardy inequalities within half-spaces, using a novel non-linear, non-local ground state representation method to improve understanding of fractional Sobolev spaces.

Contribution

It provides the first sharp constant for fractional Hardy inequalities in half-spaces, advancing the theoretical framework for fractional Sobolev spaces.

Findings

Determined the sharp constant in fractional Hardy inequalities for half-spaces.

Developed a non-linear, non-local ground state representation approach.

Enhanced the theoretical understanding of fractional Sobolev spaces.

Abstract

We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces on half-spaces. Our proof relies on a non-linear and non-local version of the ground state representation.