Concentration-Compactness Principle for Generalized Trudinger Inequalities

Abstract

Let $\Omega \subset {\mathbb{R}}^n$, $n\ge 2$, be a bounded domain and let $\alpha <n-1$. We prove the Concentration-Compactness Principle for the embedding of the Orlicz-Sobolev space $W_0^1{L}^n{\log }^{\alpha }L(\Omega )$ into the Orlicz space with the Young function $\exp \left(t^{\frac{n}{n-1-\alpha }}\right)-1$.