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Publication Date:
May 2010
ISSN:
1435-5345
DOI:
10.1515/crelle.2010.057

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Journal für die reine und angewandte Mathematik

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Homeomorphisms in the Sobolev space W1,n–1

Marianna Csörnyei1 / Stanislav Hencl2 / Jan Malý34

1Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom. e-mail: mari@math.ucl.ac.uk

2Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00 Prague 8, Czech Republic. e-mail: hencl@karlin.mff.cuni.cz

3Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00 Prague 8, Czech Republic

4Department of Mathematics, J. E. Purkyně University, České mládeže 8, 400 96 Ústí nad Labem, Czech Republic. e-mail: maly@karlin.mff.cuni.cz

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2010, Issue 644, Pages 221–235, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle.2010.057, May 2010

Publication History:
Received:
2007-09-26
Revised:
2009-03-27
Published Online:
2010-05-31

Abstract

Let be open. We show that each homeomorphism satisfies . If we moreover assume that ƒ has finite distortion, then and ƒ–1 has finite distortion. The main ingredient is a new result on change of variables in integral (area and coarea formula) for such mappings.

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