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Profile decomposition in Sobolev spaces of non-compact manifolds

  • Kunnath Sandeep
  • Cyril TintarevEmail author
Article
  • 24 Downloads

Abstract

For many known non-compact embeddings of two Banach spaces \(E\hookrightarrow F\), every bounded sequence in E has a subsequence that takes form of a profile decomposition—a sum of clearly structured terms with asymptotically disjoint supports plus a remainder that vanishes in the norm of F. In this paper we construct a profile decomposition for arbitrary sequences in the Sobolev space \(H^{1,2}(M)\) of a Riemannian manifold with bounded geometry, relative to the embedding of \(H^{1,2}(M)\) into \(L^{2^*}(M)\), generalizing the well-known profile decomposition of Struwe (Math Z 187:511–517, 1984, Proposition 2.1) to the case of general bounded sequence and a non-compact manifold.

Keywords

Concentration compactness Profile decompositions Multiscale analysis 

Mathematics Subject Classification

46E35 46B50 58J99 35B44 35A25 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.TIFR Centre for Applicable MathematicsBangaloreIndia
  2. 2.UppsalaSweden

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