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The harmonic mapping problem and affine capacity

Published online by Cambridge University Press:  26 September 2011

Tadeusz Iwaniec ,
Leonid V. Kovalev  and
Jani Onninen
Tadeusz Iwaniec
Affiliation:
Department of Mathematics, Syracuse University, 215 Carnegie, Syracuse, NY 13244, USA and Department of Mathematics and Statistics, University of Helsinki, 00014 Helsinki, Finland ([email protected])
Leonid V. Kovalev
Affiliation:
Department of Mathematics, Syracuse University, 215 Carnegie, Syracuse, NY 13244, USA ([email protected]; [email protected])
Jani Onninen
Affiliation:
Department of Mathematics, Syracuse University, 215 Carnegie, Syracuse, NY 13244, USA ([email protected]; [email protected])
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Abstract

The harmonic mapping problem asks when there exists a harmonic homeomorphism between two given domains. It arises in the theory of minimal surfaces and in the calculus of variations, specifically in hyperelasticity theory. We investigate this problem for doubly connected domains in the plane, where it already presents a considerable challenge and leads to several interesting open questions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 5 , October 2011 , pp. 1017 - 1030
Copyright
Copyright © Royal Society of Edinburgh 2011

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