The Courant-Herrmann conjecture

dc.contributor.authorGladwell, Graham M. L.
dc.contributor.authorZhu, Hongmei
dc.date.accessioned2007-03-29T23:54:51Z
dc.date.available2007-03-29T23:54:51Z
dc.date.issued2003
dc.description.abstractThe Courantā€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.
dc.identifier.citationGladwell, G. and Zhu, H. (2003), The Courantā€Herrmann conjecture. Z. angew. Math. Mech., 83: 275-281. doi:10.1002/zamm.200310034
dc.identifier.issn0021-8928
dc.identifier.urihttp://hdl.handle.net/10315/929
dc.identifier.urihttps://doi.org/10.1002/zamm.200310034
dc.language.isoen
dc.publisherJournal of Applied Mathematics and Mechanics
dc.relation.urihttp://www.google.ca
dc.subjectvibration, membrane
dc.subjectcombination of modes
dc.titleThe Courant-Herrmann conjecture
dc.typeArticle

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