Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue

Ilias Ftouh

doi:10.1051/cocv/2021109

Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue

Ilias Ftouh^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We prove that among all doubly connected domains of ℝ n of the form B1\B¯ 2, where B1 and B2 are open balls of fixed radii such that B¯ 2⊂ 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.

Original language	English
Article number	6
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	28
DOIs	https://doi.org/10.1051/cocv/2021109
State	Published - 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© The authors. Published by EDP Sciences, SMAI 2022.

Keywords

Perforated domains
Steklov eigenvalues

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization
Computational Mathematics

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10.1051/cocv/2021109

Cite this

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abstract = "We prove that among all doubly connected domains of ℝ n of the form B1\textbackslash{}B¯ 2, where B1 and B2 are open balls of fixed radii such that B¯ 2⊂ 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.",

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N2 - We prove that among all doubly connected domains of ℝ n of the form B1\B¯ 2, where B1 and B2 are open balls of fixed radii such that B¯ 2⊂ 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.

AB - We prove that among all doubly connected domains of ℝ n of the form B1\B¯ 2, where B1 and B2 are open balls of fixed radii such that B¯ 2⊂ 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.

KW - Perforated domains

KW - Steklov eigenvalues

UR - https://www.scopus.com/pages/publications/85123623764

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DO - 10.1051/cocv/2021109

M3 - Article

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VL - 28

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

M1 - 6

ER -

Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this