The first Hadamard variation of Neumann–Poincaré eigenvalues on the sphere
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- by Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi and Erika Ushikoshi PDF
- Proc. Amer. Math. Soc. 147 (2019), 1073-1080 Request permission
Abstract:
The Neumann–Poincaré operator on the two-dimensional sphere has $\frac {1}{2(2k+1)}$, $k=0,1,2,\ldots$, as its eigenvalues and the corresponding multiplicity is $2k+1$. We consider the bifurcation of eigenvalues under deformation of domains, and show that the Frechét derivative of the sum of the bifurcations is zero. We then discuss the connection of this result with some conjectures regarding the Neumann–Poincaré operator.References
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Additional Information
- Kazunori Ando
- Affiliation: Department of Electrical and Electronic Engineering and Computer Science, Ehime University, Ehime 790-8577, Japan
- MR Author ID: 779522
- Email: ando@cs.ehime-u.ac.jp
- Hyeonbae Kang
- Affiliation: Department of Mathematics and Institute of Applied Mathematics, Inha University, Incheon 22212, South Korea
- MR Author ID: 268781
- Email: hbkang@inha.ac.kr
- Yoshihisa Miyanishi
- Affiliation: Center for Mathematical Modeling and Data Science, Osaka University, Osaka 560-8531, Japan
- MR Author ID: 633586
- ORCID: 0000-0002-8252-4267
- Email: miyanishi@sigmath.es.osaka-u.ac.jp
- Erika Ushikoshi
- Affiliation: Faculty of Environment and Information Sciences, Yokohama National University, Kanagawa 240-8501, Japan
- MR Author ID: 1018423
- Email: ushikoshi-erika-ng@ynu.ac.jp
- Received by editor(s): May 6, 2018
- Received by editor(s) in revised form: May 24, 2018
- Published electronically: December 3, 2018
- Additional Notes: This work was supported by A3 Foresight Program among China (NSF), Japan (JSPS), and Korea (NRF 2014K2A2A6000567).
The first author was supported by JSPS KAKENHI Grant JP17K05303
The second author was supported by NRF 2016R1A2B4011304 and 2017R1A4A1014735
The third author was the corresponding author
The fourth author was supported by JSPS KAKENHI grant number 26800073 - Communicated by: Mourad Ismail
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 1073-1080
- MSC (2000): Primary 47A45; Secondary 31B25
- DOI: https://doi.org/10.1090/proc/14246
- MathSciNet review: 3896057