A threshold phenomenon for embeddings of $H_0^m$ into Orlicz spaces

Abstract

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H_0^m$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H_0^m$-norms of the functions is greater than or equal to a positive geometric constant.

14 Pages

References in corpus (2)

• Classification of solutions to the higher order Liouville's equation on R^{2m}
• Concentration-compactness phenomena in the higher order Liouville's equation

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• Large blow-up sets for the prescribed Q-curvature equation in the Euclidean space