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Radial symmetry and partially overdetermined problems in a convex cone

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  • Jihye Lee
  • Keomkyo Seo

Abstract

We obtain the radial symmetry of the solution to a partially overdetermined boundary value problem in a convex cone in space forms by using the maximum principle for a suitable subharmonic function P and integral identities. In dimension 2, we prove Serrin‐type results for partially overdetermined problems outside a convex cone. Furthermore, we obtain a Rellich identity for an eigenvalue problem with mixed boundary conditions in a cone.

Suggested Citation

  • Jihye Lee & Keomkyo Seo, 2023. "Radial symmetry and partially overdetermined problems in a convex cone," Mathematische Nachrichten, Wiley Blackwell, vol. 296(3), pages 1204-1224, March.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:3:p:1204-1224
    DOI: 10.1002/mana.202000423
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