The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis-Nirenberg problem

TL;DR

This paper extends the concentration-compactness principle to fractional Sobolev spaces in unbounded domains and applies it to establish existence results for critical fractional p-Laplacian equations.

Contribution

It introduces a generalized concentration-compactness principle for fractional Sobolev spaces in unbounded domains, enabling new existence results for fractional PDEs.

Findings

Extended concentration-compactness principle for fractional Sobolev spaces

Derived sufficient conditions for solutions to fractional critical equations

Applied the principle to fractional p-Laplacian problems in al R^n

Abstract

In this paper we extend the well-known concentration -- compactness principle for the Fractional Laplacian operator in unbounded domains. As an application we show sufficient conditions for the existence of solutions to some critical equations involving the fractional $p-$laplacian in the whole ${\mathbb R}^n$.