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October 9, 2025Open Access

A note on the first Steklov eigenvalue on planar domains

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Analysis reveals closed nodal line behavior in planar domains, suggesting eigenvalue simplicity in ellipses.

The first positive Steklov eigenvalue exhibits a closed nodal line in specific planar domains.
A lower bound for the first positive eigenvalue is established in certain symmetric domains.
The eigenvalue for all ellipses is proven to be simple, enhancing previous findings.
These findings extend the theories posed by Kuttler and Sigillito in 1969 on eigenvalue behavior.

DelaTorre et al. (2025) studied this question.

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