The Courant-Herrmann conjecture

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Date

2003

Authors

Gladwell, Graham M. L.
Zhu, Hongmei

Journal Title

Journal ISSN

Volume Title

Publisher

Journal of Applied Mathematics and Mechanics

Abstract

The 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 DāˆˆRN. 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 RN(Nā‰„2), but show that it is false in general.

Description

Keywords

vibration, membrane, combination of modes

Citation

Gladwell, G. and Zhu, H. (2003), The Courantā€Herrmann conjecture. Z. angew. Math. Mech., 83: 275-281. doi:10.1002/zamm.200310034