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].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have