Fractional Hardy-Sobolev inequalities on half spaces

TL;DR

This paper studies the existence of extremal functions for fractional Hardy-Sobolev inequalities involving the Dirichlet fractional Laplacian on half-spaces, contributing to the understanding of fractional PDEs and inequalities.

Contribution

It establishes the existence of extremals for Hardy-Sobolev inequalities with the fractional Laplacian on half-spaces, a novel result in fractional analysis.

Findings

Existence of extremals for fractional Hardy-Sobolev inequalities.

Extension of classical inequalities to fractional Laplacian setting.

Insights into fractional PDEs on half-spaces.

Abstract

We investigate the existence of extremals for Hardy-Sobolev inequalities involving the Dirichlet fractional Laplacian of order s, 0<s<1, on half-spaces.