The Courant-Herrmann conjecture
| dc.contributor.author | Gladwell, Graham M. L. | |
| dc.contributor.author | Zhu, Hongmei | |
| dc.date.accessioned | 2007-03-29T23:54:51Z | |
| dc.date.available | 2007-03-29T23:54:51Z | |
| dc.date.issued | 2003 | |
| dc.description.abstract | The CourantāHerrmann 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. | |
| dc.identifier.citation | Gladwell, G. and Zhu, H. (2003), The CourantāHerrmann conjecture. Z. angew. Math. Mech., 83: 275-281. doi:10.1002/zamm.200310034 | |
| dc.identifier.issn | 0021-8928 | |
| dc.identifier.uri | http://hdl.handle.net/10315/929 | |
| dc.identifier.uri | https://doi.org/10.1002/zamm.200310034 | |
| dc.language.iso | en | |
| dc.publisher | Journal of Applied Mathematics and Mechanics | |
| dc.relation.uri | http://www.google.ca | |
| dc.subject | vibration, membrane | |
| dc.subject | combination of modes | |
| dc.title | The Courant-Herrmann conjecture | |
| dc.type | Article |