The concentration-compactness principle for Orlicz spaces and applications

TL;DR

This paper extends the concentration-compactness principle to Orlicz spaces and applies it to prove existence results for certain critical elliptic problems with nonstandard growth.

Contribution

It introduces a generalized concentration-compactness principle for Orlicz spaces, expanding its applicability beyond classical Lebesgue spaces.

Findings

Established a concentration-compactness framework for Orlicz spaces

Proved existence of solutions for critical elliptic problems with nonstandard growth

Extended classical analysis tools to broader functional settings

Abstract

In this paper we extend the well-known concentration -- compactness principle of P.L. Lions to Orlicz spaces. As an application we show an existence result to some critical elliptic problem with nonstandard growth.