Radial symmetry and partially overdetermined problems in a convex cone

Jihye Lee and Keomkyo Seo

Mathematische Nachrichten, 2023, vol. 296, issue 3, 1204-1224

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.

Date: 2023
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https://doi.org/10.1002/mana.202000423

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