Deformations of finite conformal energy: Boundary behavior and limit theorems

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Abstract

We study homeomorphisms h Y between two bounded domains in ℝn having finite conformal energy We consider the behavior of such mappings, including continuous extension to the closure of X and injectivity of h In general, passing to the weak W 1,n-limit of a sequence of homeomorphisms h one loses injectivity. However, if the mappings in question have uniformly bounded ℒ1-average of the inner distortion, then, for sufficiently regular domains X and Y, their limit map h: X Y is a homeomorphism. Moreover, the inverse map f=h-1: Y X enjoys finite conformal energy and has integrable inner distortion as well.

Original languageEnglish (US)
Pages (from-to)5605-5648
Number of pages44
JournalTransactions of the American Mathematical Society
Volume363
Issue number11
DOIs
StatePublished - Nov 2011

Keywords

  • Boundary behavior of homeomorphisms
  • Energy integrals
  • Limit theorems
  • Quasiconformal hyperelasticity

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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