A1 Journal article (refereed)
Radial symmetry of minimizers to the weighted Dirichlet energy (2021)
Koski, A., & Onninen, J. (2021). Radial symmetry of minimizers to the weighted Dirichlet energy. Proceedings of the Royal Society of Edinburgh section A : Mathematics, 151(1), 169-186. https://doi.org/10.1017/prm.2020.8
JYU authors or editors
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: 2021
Volume: 151
Issue number: 1
Pages range: 169-186
Publisher: RSE Scotland Foundation
Publication country: United Kingdom
Publication language: English
DOI: https://doi.org/10.1017/prm.2020.8
Publication open access: Not open
Publication channel open access:
Web address of parallel published publication (pre-print): https://arxiv.org/abs/1904.08213
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: partial differential equations; complex analysis; calculus of variations
Free keywords: variational integrals; harmonic mappings; energy-minimal deformations
Contributing organizations
Related projects
- InvProbGeomPDE Inverse Problems in Partial Differential Equations and Geometry
- Salo, Mikko
- European Commission
Ministry reporting: Yes
Reporting Year: 2021
JUFO rating: 1