A note on the first Steklov eigenvalue on planar domains
Analysis of PDEs
2026-03-23 v1
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).
Cite
@article{arxiv.2507.23312,
title = {A note on the first Steklov eigenvalue on planar domains},
author = {Azahara DelaTorre and Gabriele Mancini and Angela Pistoia and Luigi Provenzano},
journal= {arXiv preprint arXiv:2507.23312},
year = {2026}
}