Global compactness results for fractional $p$-Laplace Hardy Sobolev operator on a bounded domain

TL;DR

This paper proves a global compactness result for a class of nonlinear critical Hardy-Sobolev problems involving the fractional p-Laplace Hardy operator on bounded domains, advancing understanding of solution behavior in fractional Sobolev spaces.

Contribution

It establishes a Struwe type global compactness result specifically for fractional p-Laplace Hardy-Sobolev operators, a novel extension in the analysis of nonlinear critical problems.

Findings

Proved a Struwe type global compactness theorem for fractional p-Laplace Hardy-Sobolev problems.

Extended compactness results to fractional Hardy-Sobolev operators on bounded domains.

Enhanced understanding of solution structure for nonlinear critical fractional PDEs.

Abstract

In this paper, we establish a Struwe type global compactness result for a class of nonlinear critical Hardy-Sobolev exponent problems driven by the fractional $p$-Laplace Hardy-Sobolev operator.