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arXiv · 2009.00280

Radial symmetry and partially overdetermined problems in a convex cone

Jihye Lee·Keomkyo Seo
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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.

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Jihye Lee, Keomkyo Seo. 2020-09-01. Radial symmetry and partially overdetermined problems in a convex cone. https://arxiv.org/abs/2009.00280

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