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Sharp isoperimetric upper bounds for planar Steklov eigenvalues

Girouard, Alexandre and Karpukhin, Mikhail and Lagacé, Jean (2020) Sharp isoperimetric upper bounds for planar Steklov eigenvalues. . (Unpublished)

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We solve the isoperimetric problem for the first and second nonzero Steklov eigenvalues of planar domains, without any assumption on the number of connected components of the boundary. Our approach uses the known sharp upper bounds for the weighted Neumann eigenvalues, and a homogenisation method allowing to approximate these eigenvalues by the Steklov eigenvalues of appropriately chosen perforated subdomains.

Item Type:Report or Paper (Discussion Paper)
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Record Number:CaltechAUTHORS:20201123-142739007
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106794
Deposited By: Tony Diaz
Deposited On:23 Nov 2020 22:34
Last Modified:23 Nov 2020 22:34

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