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arXiv · 1009.1502

Closed nodal surfaces for simply connected domains in higher dimensions

J. B. Kennedy
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Abstract

We give an example of a domain in dimension $N \geq 3$, homeomorphic to a ball and with analytic boundary, for which the second eigenvalue of the Dirichlet Laplacian has an eigenfunction with a closed nodal surface. The domain is constructed via a sequence of perturbations of the domain of S. Fournais [J. Differential Equations \textbf{173} (2001), 145-159].

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J. B. Kennedy. 2010-09-08. Closed nodal surfaces for simply connected domains in higher dimensions. https://arxiv.org/abs/1009.1502

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