| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 6 | |
| Number of page(s) | 21 | |
| DOI | https://doi.org/10.1051/cocv/2021109 | |
| Published online | 17 January 2022 | |
Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue
Friedrich-Alexander-Universität Erlangen-Nürnberg,
Erlangen, Germany.
* Corresponding author: ilias.ftouhi@fau.de
Received:
28
August
2021
Accepted:
22
December
2021
We prove that among all doubly connected domains of ℝn of the form B1\B̅2, where B1 and B2 are open balls of fixed radii such that B̅2⊂B1, the first nonzero Steklov eigenvalue achieves its maximal value uniquely when the balls are concentric. Furthermore, we show that the ideas of our proof also apply to a mixed boundary conditions eigenvalue problem found in literature.
Mathematics Subject Classification: 49R50 / 49Q10 / 35P05
Key words: Steklov eigenvalues / perforated domains
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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