Closed nodal surfaces for simply connected domains in higher dimensions

Details Closed nodal surfaces for simply connected domains in higher dimensions Closed nodal surfaces for simply connected domains in higher dimensions

2010-09-08

arxiv.org/abs/1009.1502v1

Mathematics

Analysis of PDEs

10 pages

Scientific paper

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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