The harmonic mapping problem and affine capacity

The harmonic mapping problem and affine capacity

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...

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Veröffentlicht in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2011-10, Vol.141 (5), p.1017-1030
Hauptverfasser: Iwaniec, Tadeusz, Kovalev, Leonid V., Onninen, Jani
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of variations
Elasticity
Harmonic analysis
Harmonics
Mapping
Mathematical analysis
Mathematics
Minimal surfaces
Planes
Theorems
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Zusammenfassung: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.
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210510000107