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

Ilias Ftouhi (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We prove that the first non-trivial Steklov eigenvalue of a spherical shell is maximal when the balls are concentric. We also show that the ideas used may apply to a mixed boundary conditions eigenvalue problem found in literature.

Domains: Analysis of PDEs [math.AP]; Optimization and Control [math.OC]; Classical Analysis and ODEs [math.CA]

Ilias Ftouhi. Where to place a spherical obstacle so as to maximize the first Steklov eigenvalue. 2019. ⟨hal-02334941v3⟩