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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On compact subsets of Sobolev spaces on manifolds
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by Leszek Skrzypczak and Cyril Tintarev PDF
Trans. Amer. Math. Soc. 374 (2021), 3761-3777 Request permission

Abstract:

The paper considers compactness of Sobolev embeddings of non-compact manifolds, restricted to subsets (typically subspaces) defined either by conditions of symmetry (or quasisymmetry) relative to actions of compact groups, or by restriction in the number of variables, i.e. consisting of functions of the form $f\circ \varphi$ with a fixed $\varphi$. The manifolds are assumed to satisfy general common conditions under which Sobolev embeddings exist. We provide sufficient conditions for compactness of the embeddings, which in many situations are also necessary.
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Additional Information
  • Leszek Skrzypczak
  • Affiliation: Faculty of Mathematics & Computer Science, Adam Mickiewicz University, ul. Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland
  • MR Author ID: 292730
  • ORCID: 0000-0002-7484-2900
  • Email: lskrzyp@amu.edu.pl
  • Cyril Tintarev
  • Affiliation: Technion – Israel Institute of Technology, Haifa 32000, Israel
  • MR Author ID: 172775
  • ORCID: 0000-0002-7484-2900
  • Email: tammouz@gmail.com
  • Received by editor(s): August 5, 2020
  • Received by editor(s) in revised form: October 22, 2020
  • Published electronically: March 2, 2021
  • Additional Notes: The first author was supported by National Science Center, Poland, Grant no. 2013/10/A/ST1/00091.
    The second author expresses his gratitude to the first author and the Faculty of Mathematics & Computer Science of Adam Mickiewicz University, as well as to Simeon Reich, Yehuda Pinchover and the Faculty of Mathematics at Technion, for their kind hospitality. The latter stay was as a Lady Davis Visiting Professor.
  • © Copyright 2021 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 374 (2021), 3761-3777
  • MSC (2020): Primary 46B50, 46E35; Secondary 46N20
  • DOI: https://doi.org/10.1090/tran/8322
  • MathSciNet review: 4237962