2019年11月1日
Spectral structure of the Neumann–Poincar\´e operator on tori
Annales de l'Institut Henri Poincaré C, Analyse non linéaire
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プレプリント・著者最終稿
回数 : 197
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- 巻
- 36
- 号
- 7
- 開始ページ
- 1817
- 終了ページ
- 1828
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1016/j.anihpc.2019.05.002
We address the question whether there is a three-dimensional bounded domain such that the Neumann--Poincaré operator defined on its boundary has infinitely many negative eigenvalues. It is proved in this paper that tori have such a property. It is done by decomposing the Neumann--Poincaré operator on tori into infinitely many self-adjoint compact operators on a Hilbert space defined on the circle using the toroidal coordinate system and the Fourier basis, and then by proving that the numerical range of infinitely many operators in the decomposition has both positive and negative values.
- リンク情報
- ID情報
-
- DOI : 10.1016/j.anihpc.2019.05.002
- ORCIDのPut Code : 56297827
- arXiv ID : arXiv:1810.09693