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<p>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 <CitationRef CitationID="CR14">1969</CitationRef>).</p>

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A NOTE ON THE FIRST STEKLOV EIGENVALUE ON PLANAR DOMAINS

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Azahara DelaTorre,
  • Gabriele Mancini,
  • Angela Pistoia,
  • Luigi Provenzano

摘要

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).