Some overdetermined problems related to the anisotropic capacity

Giulio Ciraolo, Chiara Bianchini, Paolo Salani

Research output: Contribution to journalArticlepeer-review

Abstract

We characterize the Wulff shape of an anisotropic norm in terms of solutions to overdetermined problems for the Finsler p-capacity of a convex set Ω⊂RN, with 1<p<N. In particular we show that if the Finsler p-capacitary potential u associated to Ω has two homothetic level sets then Ω is Wulff shape. Moreover, we show that the concavity exponent of u is q=−(p−1)/(N−p) if and only if Ω is Wulff shape.
Original languageEnglish
Pages (from-to)211-219
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume465
Publication statusPublished - 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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