Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 60, Issue 3, Pages 1546-1562Publisher
SIAM PUBLICATIONS
DOI: 10.1137/21M1411925
Keywords
Steklov eigenvalues; perturbation theory; isoperimetric inequality
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Funding
- NSF DMS [17-52202]
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We investigate the Steklov eigenvalues of three-dimensional nearly spherical domains. Previous research has shown that these eigenvalues depend analytically on the domain perturbation parameter. In this study, we compute the first-order term of the asymptotic expansion using the Wigner 3-j symbols. We analyze the expansion and demonstrate the isoperimetric result that the volume-normalized \ell th Steklov eigenvalue is stationary for a ball when \ell is a perfect square.
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-j symbols. We analyze the asymptotic expansion and prove the isoperimetric result that, if \ell is a square integer, the volume-normalized \ell th Steklov eigenvalue is stationary for a ball.
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