A Remark on the Concentration Compactness Principle in Critical Dimension

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Abstract

We prove some refinements of the concentration compactness principle for Sobolev space W1, n on a smooth compact Riemannian manifold of dimension n. As an application, we extend Aubin's theorem for functions on (Formula presented.) with zero first-order moments of the area element to the higher-order moments case. Our arguments are very flexible and can be easily modified for functions satisfying various boundary conditions or belonging to higher-order Sobolev spaces.

Original languageEnglish (US)
Pages (from-to)2245-2278
Number of pages34
JournalCommunications on Pure and Applied Mathematics
Volume75
Issue number10
DOIs
StatePublished - Oct 2022

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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