Limits of Sobolev homeomorphisms

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16 Scopus citations


Let X,Y R2 be topologically equivalent bounded Lipschitz domains. We prove that weak and strong limits of homeomorphisms h: X onto → Y in the Sobolev space W 1,p(X,R2), p ≥ 2; are the same. As an application, we establish the existence of 2D-traction free minimal deformations for fairly general energy integrals.

Original languageEnglish (US)
Pages (from-to)473-505
Number of pages33
JournalJournal of the European Mathematical Society
Issue number2
StatePublished - 2017


  • Approximation of Sobolev homeomorphisms
  • Energy-minimal deformations
  • Harmonic mappings
  • P-harmonic equation
  • Variational integrals

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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