A threshold phenomenon for embeddings of $H^m_0$ into Orlicz spaces

preprint2009arXivOpen access

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H^m_0$ -norms of the functions is greater than or equal to a positive geometric constant.

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A threshold phenomenon for embeddings of $H^m_0$ into Orlicz spaces

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A threshold phenomenon for embeddings of $H^m_0$ into Orlicz spaces