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)
JournalCommunications on Pure and Applied Mathematics
DOIs
StateAccepted/In press - 2021

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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