A1 Journal article (refereed)
Radial symmetry of minimizers to the weighted Dirichlet energy (2020)


Koski, Aleksis; Onninen, Jani (2020). Radial symmetry of minimizers to the weighted Dirichlet energy. Proceedings of the Royal Society of Edinburgh section A : Mathematics, Early online. DOI: 10.1017/prm.2020.8


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Publication details

All authors or editors: Koski, Aleksis; Onninen, Jani

Journal or series: Proceedings of the Royal Society of Edinburgh section A : Mathematics

ISSN: 0308-2105

eISSN: 1473-7124

Publication year: 2020

Volume: Early online

Publisher: RSE Scotland Foundation

Publication country: United Kingdom

Publication language: English

DOI: http://doi.org/10.1017/prm.2020.8

Open Access: Publication channel is not openly available


Abstract

We consider the problem of minimizing the weighted Dirichlet energy between homeomorphisms of planar annuli. A known challenge lies in the case when the weight λ depends on the independent variable z. We prove that for an increasing radial weight λ(z) the infimal energy within the class of all Sobolev homeomorphisms is the same as in the class of radially symmetric maps. For a general radial weight λ(z) we establish the same result in the case when the target is conformally thin compared to the domain. Fixing the admissible homeomorphisms on the outer boundary we establish the radial symmetry for every such weight.


Keywords: integral calculus

Free keywords: variational integrals; harmonic mappings; energy-minimal deformations


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Last updated on 2020-09-07 at 23:13