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 a work by Kuttler and Sigillito (Proc. Amer. Math. Soc. 20, 1969).
A note on the first Steklov eigenvalue on planar domains / Delatorre, Azahara; Mancini, Gabriele; Pistoia, Angela; Provenzano, Luigi. - In: JOURNAL OF MATHEMATICAL SCIENCES. - ISSN 1573-8795. - (2026). [10.1007/s10958-026-08225-5]
A note on the first Steklov eigenvalue on planar domains
Azahara DelaTorre;Angela Pistoia
;Luigi Provenzano
2026
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 a work by Kuttler and Sigillito (Proc. Amer. Math. Soc. 20, 1969).| File | Dimensione | Formato | |
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