Approximation up to the boundary of homeomorphisms of finite Dirichlet energy

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5 Scopus citations

Abstract

Let ⊂ and ⊂ be Jordan domains of the same finite connectivity, being inner chordarc regular (such are Lipschitz domains). Every homeomorphism h: → in the Sobolev space 1, 2 extends to a continuous map h: →. We prove that there exist homeomorphisms hk: → that converge to h uniformly and in 1, 2. The problem of approximation of Sobolev homeomorphisms, raised by J. M. Ball and L. C. Evans, is deeply rooted in a study of energy-minimal deformations in non-linear elasticity. The new feature of our main result is that approximation takes place also on the boundary, where the original map need not be a homeomorphism.

Original languageEnglish (US)
Pages (from-to)871-881
Number of pages11
JournalBulletin of the London Mathematical Society
Volume44
Issue number5
DOIs
StatePublished - Oct 2012

ASJC Scopus subject areas

  • Mathematics(all)

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