Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains (Q1327477)
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scientific article; zbMATH DE number 590902
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains |
scientific article; zbMATH DE number 590902 |
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Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains (English)
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30 May 1996
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Summary: We describe the boundary behavior of the nodal lines of eigenfunctions of the fixed membrane problem in convex, possibly nonsmooth, domains. This result is applied to the proof of Payne's conjecture on the nodal line of second eigenfunctions, by removing the \(C^\infty\) smoothness assumption which is present in the original proof of \textit{A. D. Melas} [J. Differ. Geom. 35, No. 1, 255-263 (1992; Zbl 0769.58056)].
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boundary behavior of nodal lines
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second eigenfunctions
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