- 97-417 Hoffmann-Ostenhof M., Hoffmann-Ostenhof T., Nadirashvili N.
- On the Nodal Line Conjecture
Jul 24, 97
(auto. generated ps),
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Abstract. We consider Dirichlet eigenfunctions of membrane problems. A counterexample
to Payne's nodal line conjecture is given, i.e. a domain in $\mathbb R^2$
(not simply connected) whose second eigenfunction has a nodal set disjoint
from the boundary. Also a domain in $\mathbb R^2$ is given whose second
eigenvalue has multiplicity three.
Furthermore, some sufficient conditions are given which imply that an
eigenfunction of a Dirichlet membrane problem in $\mathbb R^n$ has a zero
set which hits the boundary.