6533b872fe1ef96bd12d36ad
RESEARCH PRODUCT
Radial symmetry of minimizers to the weighted Dirichlet energy
Aleksis KoskiJani Onninensubject
Class (set theory)Computer Science::Information RetrievalGeneral Mathematics010102 general mathematicsMathematical analysisSymmetry in biologyBoundary (topology)Dirichlet's energy01 natural sciencesDomain (mathematical analysis)010101 applied mathematicsSobolev spacePlanar0101 mathematicsEnergy (signal processing)Mathematicsdescription
AbstractWe 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-02-20 | Proceedings of the Royal Society of Edinburgh: Section A Mathematics |