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Regularity of the inverse of a Sobolev homeomorphism in space

Published online by Cambridge University Press:  12 July 2007

Stanislav Hencl ,
Pekka Koskela  and
Jan Malý
Stanislav Hencl
Affiliation:
Department of Mathematics and Statistics, University of Jyväskylä, PO Box 35 (MaD), 40014 Jyväskylä, Finlandhencl@maths.jyu.fi
Pekka Koskela
Affiliation:
Department of Mathematics and Statistics, University of Jyväskylä, PO Box 35 (MaD), 40014 Jyväskylä, Finlandpkoskela@maths.jyu.fi
Jan Malý
Affiliation:
Department of Mathematical Analysis, Charles University, Sokolovská 83, 18600 Prague 8, Czech Republic and Department of Mathematics, Faculty of Science, J. E. Purkyně University, České mládeže 8, 40096 Ústí nad Labem, Czech Republic (maly@karlin.mff.cuni.cz)
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Abstract

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Let Ω ⊂ Rn be open. Given a homeomorphism of finite distortion with |Df| in the Lorentz space Ln−1, 1 (Ω), we show that and f−1 has finite distortion. A class of counterexamples demonstrating sharpness of the results is constructed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 6 , December 2006 , pp. 1267 - 1285
Copyright
Copyright © Royal Society of Edinburgh 2006