Abstract

This paper compares the eigenvalues arising from the vibration of an inhomogeneous circular membrane with the eigenvalues of a homogeneous circular membrane having the same total mass. Assume that on each concentric subdisk the inhomogeneous membrane has at least as much mass as the homogeneous membrane. Then the first eigenvalue of the whole disk (with Dirichlet boundary conditions) is maximal for the homogeneous membrane. Furthermore, the zeta function of the eigenvalues is minimal for the homogeneous disk. Corollaries follow for simply connected surfaces with nonnegative curvature. Stronger results hold in one dimension, for vibrating strings.

pdf

Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 305-344
Launched on MUSE
1998-04-01
Open Access
No
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.