An overdetermined problem for the anisotropic capacity

Giulio Ciraolo, Chiara Bianchini, Paolo Salani

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

We consider an overdetermined problem for the Finsler Laplacian in the exterior of a convex domain in RN, establishing a symmetry result for the anisotropic capacitary potential. Our result extends the one of Reichel (Arch Ration Mech Anal 137(4):381–394, 1997), where the usual Newtonian capacity is considered, giving rise to an overdetermined problem for the standard Laplace equation. Here, we replace the usual Euclidean norm of the gradient with an arbitrary norm H. The resulting symmetry of the solution is that of the so-called Wulff shape (a ball in the dual norm H0).
Original languageEnglish
Number of pages24
JournalCalculus of Variations and Partial Differential Equations
Volume55
Publication statusPublished - 2016

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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