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

2025/01/04 by Ilias Ftouhi, Ftouhi, Ilias · 1 citation
Computer Science · Mathematics · #Algebraic and Geometric Analysis #Computer Graphics and Visualization Techniques #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2501.02289

openalex publication_date 2025/01/04 · openalex created_date 2025/01/08 · openalex updated_date 2026/07/28

Abstract

We prove that among all doubly connected domains of ℝⁿ of the form B₁\backslash B₂, where B₁ and B₂ are open balls of fixed radii such that B₂⊂ 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.

Cited by

• Sensor placement via large deviations in the Eikonal equation

Related

• Shape optimization for the Steklov problem in higher dimensions
• Sharp upper bound and a comparison theorem for the first nonzero Steklov eigenvalue
• Bounds for the first non-zero Steklov eigenvalue
• Maximization of the Steklov eigenvalues with a diameter constraint
• An upper bound for the first nonzero Steklov eigenvalue