Steklov Eigenvalues of Nearly Spherical Domains

2021/04/07 by Robert Viator, Viator, Robert, Braxton Osting +1 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #math.AP #math.SP

paper · pdf · doi:10.48550/arxiv.2104.03380

arxiv created 2021/04/07 · arxiv updated 2021/04/09

Abstract

We consider Steklov eigenvalues of three-dimensional, nearly-spherical domains. In previous work, we have shown that the Steklov eigenvalues are analytic functions of the domain perturbation parameter. Here, we compute the first-order term of the asymptotic expansion, which can explicitly be written in terms of the Wigner 3-jsymbols. We analyze the asymptotic expansion and prove the isoperimetric result that, if l is a square integer, the volume-normalized l-th Steklov eigenvalue is stationary for a ball.

Cited by

• Extremal Steklov-Neumann Eigenvalues
• Steklov eigenvalues of nearly circular area-normalized domains

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