We consider the first positive Steklov eigenvalue on planar domains. First, we provide an example of a planar domain for which a first eigenfunction has a closed nodal line. Second, we establish a lower bound for the first positive eigenvalue on certain symmetric domains and show that this eigenvalue is simple for all ellipses. These results complement two statements contained in Kuttler and Sigillito (Proc. Amer. Math. Soc. 20 1969).
A NOTE ON THE FIRST STEKLOV EIGENVALUE ON PLANAR DOMAINS
Mancini, Gabriele;
2026-01-01
Abstract
We consider the first positive Steklov eigenvalue on planar domains. First, we provide an example of a planar domain for which a first eigenfunction has a closed nodal line. Second, we establish a lower bound for the first positive eigenvalue on certain symmetric domains and show that this eigenvalue is simple for all ellipses. These results complement two statements contained in Kuttler and Sigillito (Proc. Amer. Math. Soc. 20 1969).File in questo prodotto:
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