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• W2222636700 abstract "We develop a computational method for extremal Steklov eigenvalue problems and apply it to study the problem of maximizing the $p$th Steklov eigenvalue as a function of the domain with a volume constraint. In contrast to the optimal domains for several other extremal Dirichlet- and Neumann-Laplacian eigenvalue problems, computational results suggest that the optimal domains for this problem are very structured. We reach the conjecture that the domain maximizing the $p$th Steklov eigenvalue is unique (up to dilations and rigid transformations), has $p$-fold symmetry, and has at least one axis of symmetry. The $p$th Steklov eigenvalue has multiplicity 2 if $p$ is even and multiplicity 3 if $pgeq3$ is odd." @default.
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• W2222636700 date "2017-01-01" @default.
• W2222636700 modified "2023-10-08" @default.
• W2222636700 title "Computational Methods for Extremal Steklov Problems" @default.
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• W2222636700 doi "https://doi.org/10.1137/16m1067263" @default.
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