A concavity condition for existence of a negative Neumann-Poincar\'e eigenvalue in three dimensions
| Autor: | Ji, Yong-Gwan, Kang, Hyeonbae |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | It is proved that if a bounded domain in three dimensions satisfies a certain concavity condition, then the Neumann-Poincar\'e operator on the boundary of the domain or its inversion in a sphere has at least one negative eigenvalue. The concavity condition is quite simple, and is satisfied if there is a point on the boundary at which the Gaussian curvature is negative. |
| Databáze: | arXiv |
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