IUMJ

Title: Closed nodal surfaces for simply connected domains in higher dimensions

Authors: James Kennedy

Issue: Volume 62 (2013), Issue 3, 785-798

Abstract:

We give an example of a domain in dimension $N\geq3$, 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].