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On the nodal lines of second eigenfunctions of the fixed membrane problem

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Commentarii Mathematici Helvetici

Abstract

A well-known conjecture about the second eigenfunction of a bounded domain in ℝ2 states that the nodal line has to intersect the boundary in exactly two points. We give sufficient conditions on the domain for this assertion to hold. For special doubly symmetric domains we also prove that λ2 is simple and that the nodal line of the second eigenfunction lies on one of the axes.

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Authors and Affiliations

  1. FB9 Universität des Saarlandes, D-6600, Saarbrücken, Germany

    Rolf Pütter

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  1. Rolf Pütter
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Pütter, R. On the nodal lines of second eigenfunctions of the fixed membrane problem. Commentarii Mathematici Helvetici 65, 96–103 (1990). https://doi.org/10.1007/BF02566596

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  • DOI: https://doi.org/10.1007/BF02566596

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