A Critical Domain For the First Normalized Nontrivial Steklov Eigenvalue Among Planar Annular Domains

Abstract

We describe a shape derivative approach to provide a candidate for an optimal domain among non-simply connected planar domains with two boundary components. This approach is an adaptation of the work on the extremal eigenvalue problem for the Wentzell-Laplace operator developed by Dambrine, Kateb and Lamboley.

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