On the second eigenfunctions of the Laplacian in R2
Journal
Communications in Mathematical Physics
Journal Volume
111
Journal Issue
2
Pages
161-166
Date Issued
1987
Author(s)
Abstract
A conjecture about the nodal line of a second eigenfunction states that the nodal line of a second eigenfunction divides the domain Ω by intersecting with the boundary of Ω transversely, where Ω is a bounded convex domain of R2. We prove this conjecture provided Ω has a symmetry. Also, we prove the multiplicity of the second eigenvalue is two at most provided Ω is a bounded convex domain of R2. © 1987 Springer-Verlag.
Type
journal article