On generalization of Moser's theorem in the critical case

Abstract

We study Moser's theorem concerning embedding of Sobolev spaces into exponential Orlicz spaces. In case of the critical power, we find the borderline Young function so that the Moser's embedding holds for the corresponding Orlicz-Sobolev space.

Keywords

• Orlicz spaces
• Orlicz-Sobolev spaces
• embedding theorems
• sharp constants