Concentration-Compactness Principle for Generalized Trudinger Inequalities

Abstract

Let $\Omega\subset\mathbb R^n$, $n\geq 2$, be a bounded domain and let $\alpha < n-1$. We prove the Concentration-Compactness Principle for the embedding of the Orlicz-Sobolev space $W^1_0L^n\log^{\alpha}L(\Omega)$ into the Orlicz space with the Young function $\exp\big(t^{\frac{n}{n-1-\alpha}}\big)-1$.