Steklov Eigenvalues of Nearly Spherical Domains

Robert Viator; Braxton Osting

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arXiv · 2104.03380

Steklov Eigenvalues of Nearly Spherical Domains

Robert Viator·Braxton Osting

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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.

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Robert Viator, Braxton Osting. 2021-04-07. Steklov Eigenvalues of Nearly Spherical Domains. https://arxiv.org/abs/2104.03380

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