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arXiv · 2109.01884

Numerical calculation of extremal Steklov eigenvalues in 3D and 4D

Pedro R. S. Antunes
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Abstract

We develop a numerical method for solving shape optimization of functionals involving Steklov eigenvalues and apply it to the problem of maximization of the $k$-th Steklov eigenvalue, under volume constraint. A similar study in the planar case was addressed in [E. Akhmetgaliyev, C.-Y. Kao and B. Osting, SIAM J. Control Optim. 55(2), 1226-1240, (2017)] using the boundary integral equation method. Here we extend that study to the 3D and 4D cases, using the Method of Fundamental Solutions as forward solver.

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Pedro R. S. Antunes. 2021-09-04. Numerical calculation of extremal Steklov eigenvalues in 3D and 4D. https://arxiv.org/abs/2109.01884

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