Jacobian of weak limits of Sobolev homeomorphisms

Stanislav Hencl, Jani Onninen

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Let Ω be a domain in ℝn, where n = 2, 3. Suppose that a sequence of Sobolev homeomorphisms fk : Ω → ℝn with positive Jacobian determinants, J(x, fk) > 0, converges weakly in W1,p(Ω, ℝn), for some p ≥ 1, to a mapping f. We show that J(x, f) ≥ 0 a.e. in Ω. Generalizations to higher dimensions are also given.

Original languageEnglish (US)
Pages (from-to)65-73
Number of pages9
JournalAdvances in Calculus of Variations
Volume11
Issue number1
DOIs
StatePublished - Jan 1 2018

Keywords

  • Jacobian
  • Sobolev homeomorphism
  • weak limits

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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