Boundary Perturbations of Steklov Eigenvalues

TL;DR

This paper investigates how smooth boundary perturbations affect Steklov eigenvalues, proving that such eigenvalues are typically simple under these variations, complementing prior results on metric perturbations.

Contribution

It establishes that non-zero Steklov eigenvalues are generically simple under smooth boundary perturbations, extending previous work on metric perturbations.

Findings

Steklov eigenvalues are generically simple under boundary perturbations

Results complement previous work on metric perturbations

Provides a unified understanding of eigenvalue simplicity under geometric variations

Abstract

We consider the dependence of non-zero Steklov eigenvalues on smooth perturbations of the domain boundary. We prove that these eigenvalues are generically simple under such boundary perturbations. This result complements our previous work on metric perturbations, thereby establishing generic simplicity Steklov eigenvalues under both fundamental geometric variations.