Mappings of finite distortion: Compactness

Research output: Contribution to journalArticle

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Abstract

We study mappings f: Ω ↠ Rn whose distortion functions Kl(x,f), l = 1, 2, . . . , n - 1, are in general unbounded but subexponentially integrable. The main result is the weak compactness principle. It asserts that a family of mappings with prescribed volume integral ∫ Ω J(x, f) dx, and with given subexponential norm ∥1√KlExpA of a distortion function, is closed under weak convergence. The novelty of this result is twofold. Firstly, it requires integral bounds on the distortions Kl(x, f) which are weaker than those for the usual outer distortion. Secondly, the category of subexponential bounds is optimal to fully describe the compactness principle for mappings of unbounded distortion, even when outer distortion is used.

Original languageEnglish (US)
Pages (from-to)391-417
Number of pages27
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume27
Issue number2
StatePublished - Dec 31 2002

ASJC Scopus subject areas

  • Mathematics(all)

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