Steklov eigenvalues of nearly circular area-normalized domains

2025/04/30 by Alland, Lucas, Viator, Robert · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.21768

Abstract

We consider Steklov eigenvalues of nearly circular domains in \R² of fixed unitary area. In \citeviator2018, the authors treated such domains as perturbations of the disk, and they computed the first-order term of the asymptotic expansions of the Steklov eigenvalues for reflection-symmetric perturbations; here, we expand these first-order results beyond reflection-symmetry. We also recover the second-order asymptotic expansions, which enable us to prove that no Steklov eigenvalue beyond the first positive one is locally shape-optimized by the disk.

Citations

• Steklov eigenvalues of nearly hyperspherical domains
• Some recent developments on the Steklov eigenvalue problem
• Steklov Eigenvalues of Nearly Spherical Domains
• Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems
• Analyticity of Steklov eigenvalues of nearly-circular and nearly-spherical domains
• Shape optimization for the Steklov problem in higher dimensions
• Spectral geometry of the Steklov problem

Cited by

• Extremal Steklov-Neumann Eigenvalues

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