We prove that among all doubly connected domains of ℝ$$ of the form , where B1 and B2 are open balls of fixed radii such that , 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.
Keywords: Steklov eigenvalues, perforated domains
@article{COCV_2022__28_1_A6_0,
author = {Ftouhi, Ilias},
title = {Where to place a spherical obstacle so as to maximize the first nonzero {Steklov} eigenvalue},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2022},
publisher = {EDP-Sciences},
volume = {28},
doi = {10.1051/cocv/2021109},
mrnumber = {4364336},
zbl = {1523.35230},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021109/}
}
TY - JOUR AU - Ftouhi, Ilias TI - Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2022 VL - 28 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021109/ DO - 10.1051/cocv/2021109 LA - en ID - COCV_2022__28_1_A6_0 ER -
%0 Journal Article %A Ftouhi, Ilias %T Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue %J ESAIM: Control, Optimisation and Calculus of Variations %D 2022 %V 28 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021109/ %R 10.1051/cocv/2021109 %G en %F COCV_2022__28_1_A6_0
Ftouhi, Ilias. Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 6. doi: 10.1051/cocv/2021109
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