Radial symmetry of minimizers to the weighted Dirichlet energy

Aleksis Koski, Jani Onninen

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)169-186
Number of pages18
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Issue number1
StatePublished - Feb 2021


  • Energy-minimal deformations
  • Harmonic mappings
  • Variational integrals

ASJC Scopus subject areas

  • General Mathematics


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