The harmonic mapping problem and affine capacity

Tadeusz Iwaniec; Leonid V. Kovalev; Jani Onninen

doi:10.1017/S0308210510000107

The harmonic mapping problem and affine capacity

Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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. ©

Original language	English (US)
Pages (from-to)	1017-1030
Number of pages	14
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	141
Issue number	5
DOIs	https://doi.org/10.1017/S0308210510000107
State	Published - Oct 2011

ASJC Scopus subject areas

General Mathematics

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10.1017/S0308210510000107

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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. {\textcopyright}",

author = "Tadeusz Iwaniec and Kovalev, {Leonid V.} and Jani Onninen",

note = "Funding Information: T.I. was supported by the NSF Grant DMS-0800416 and the Academy of Finland Grant 1128331. L.V.K. was supported by the NSF Grant DMS-0913474. J.O. was supported by the NSF Grant DMS-0701059. The authors thank the anonymous referee for several helpful comments.",

year = "2011",

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T1 - The harmonic mapping problem and affine capacity

AU - Iwaniec, Tadeusz

AU - Kovalev, Leonid V.

AU - Onninen, Jani

N1 - Funding Information: T.I. was supported by the NSF Grant DMS-0800416 and the Academy of Finland Grant 1128331. L.V.K. was supported by the NSF Grant DMS-0913474. J.O. was supported by the NSF Grant DMS-0701059. The authors thank the anonymous referee for several helpful comments.

PY - 2011/10

Y1 - 2011/10

N2 - 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. ©

AB - 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. ©

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JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

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The harmonic mapping problem and affine capacity

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