Radial symmetry and partially overdetermined problems in a convex cone |
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| Authors: | Jihye Lee Keomkyo Seo |
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| Institution: | 1. Department of Mathematics, Sookmyung Women's University, Seoul, South Korea;2. Department of Mathematics and Research Institute of Natural Science, Sookmyung Women's University, Seoul, South Korea |
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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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| Keywords: | convex cone eigenvalue problem overdetermined problem P-function |
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