Mappings of L p-integrable distortion: Regularity of the inverse

Jani Onninen, Ville Tengvall

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Let be an open set in Rn and suppose that is a Sobolev homeomorphism. We study the regularity of f -1 under the L p-integrability assumption on the distortion function K f. First, if is the unit ball and p > n-1, then the optimal local modulus of continuity of f -1 is attained by a radially symmetric mapping. We show that this is not the case when p n-1 and n ≥3, and answer a question raised by S. Hencl and P. Koskela. Second, we obtain the optimal integrability results for Df -1 in terms of the L p-integrability assumptions of K f.

Original languageEnglish (US)
Pages (from-to)647-663
Number of pages17
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume146
Issue number3
DOIs
StatePublished - Jun 1 2016
Externally publishedYes

Keywords

  • Sobolev homeomorphism
  • higher integrability
  • mappings of finite distortion
  • modulus of continuity
  • regularity of the inverse

ASJC Scopus subject areas

  • Mathematics(all)

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