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Composition of bi-Sobolev homeomorphisms

Published online by Cambridge University Press:  30 January 2012

Luigi Greco ,
Carlo Sbordone  and
Roberta Schiattarella
Luigi Greco
Affiliation:
Dipartimento di Matematica e Applicazioni ‘R. Caccioppoli’, Università di Napoli ‘Frederico II’, Via Cintia, 80126 Napoli, Italy (luigreco@unina.it)
Carlo Sbordone
Affiliation:
Centro Interdisciplinare Linceo, Accademia Nazionale dei Lincei, Palazzo Corsini, Via della Lungara 10, 00165 Roma, Italy (sbordone@unina.it)
Roberta Schiattarella
Affiliation:
Dipartimento di Matematica e Applicazioni ‘R. Caccioppoli’, Università degli Studi Napoli ‘Federico II’, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy (roberta.schiattarella@unina.it)
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Abstract

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We give sharp conditions under which the composition of two homeomorphisms of finite distortion is of finite distortion and has integrable distortion. As an application, we obtain a generalization of the classical uniqueness theorem of homeomorphic solution to the measurable Riemann mapping problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 1 , February 2012 , pp. 61 - 80
Copyright
Copyright © Royal Society of Edinburgh 2012