THE FIRST HADAMARD VARIATION OF NEUMANN-POINCARE EIGENVALUES ON THE SPHERE

Ando, Kazunori; Kang, Hyeonbae; Miyanishi, Yoshihisa; Ushikoshi, Erika

doi:10.1090/proc/14246

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THE FIRST HADAMARD VARIATION OF NEUMANN-POINCARE EIGENVALUES ON THE SPHERE

Ando, Kazunori;
Kang, Hyeonbae;
Miyanishi, Yoshihisa;
Ushikoshi, Erika

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7

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7

초록

The Neumann-Poincare operator on the two-dimensional sphere has 1/2(2k+1), k = 0, 1, 2, . . . , as its eigenvalues and the corresponding multiplicity is 2k + 1. We consider the bifurcation of eigenvalues under deformation of domains, and show that the Frechet derivative of the sum of the bifurcations is zero. We then discuss the connection of this result with some conjectures regarding the Neumann- Poincare operator.

키워드

Neumann-Poincare operator; eigenvalues; Hadamard's variation formula; plasmonic eigenvalues

제목: THE FIRST HADAMARD VARIATION OF NEUMANN-POINCARE EIGENVALUES ON THE SPHERE

저자: Ando, Kazunori; Kang, Hyeonbae; Miyanishi, Yoshihisa; Ushikoshi, Erika

DOI: 10.1090/proc/14246

발행일: 2019-03

유형: Article

저널명: Proceedings of the American Mathematical Society

권: 147

호: 3

페이지: 1073 ~ 1080