Gladwell, Graham M. L.Zhu, Hongmei2007-03-292007-03-292003Gladwell, G. and Zhu, H. (2003), The Courant‐Herrmann conjecture. Z. angew. Math. Mech., 83: 275-281. doi:10.1002/zamm.2003100340021-8928http://hdl.handle.net/10315/929https://doi.org/10.1002/zamm.200310034The Courant‐Herrmann Conjecture (CHC) concerns the sign properties of combinations of the Dirichlet eigenfunctions of elliptic pde's, the most important of which is the Helmholtz equation for $D \in \mathbb{R}^N$. If the eigenvalues are ordered increasingly, CHC states that the nodal set of a combination of the first eigenfunctions, divides into no more than sign domains in which has one sign. The conjecture is classically known to hold for , we conjecture that it is true for rectangular boxes in $\mathbb{R}^N (N\geq2)$, but show that it is false in general.envibration, membranecombination of modesArticle