A Bound for the Ratio of the First Two Eigenvalues of a Membrane
- 1 November 1983
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 14 (6) , 1163-1167
- https://doi.org/10.1137/0514090
Abstract
An isoperimetric inequality for the eigenfunctions of the Laplacian is proved, using rearrangements of functions. This result, together with a technique introduced by Payne, Polya, and Weinberger (J. Math. Phys., 35 (1956), pp. 289–298), gives an upper bound (not isoperimetric) for the ratio of the first two eigenvalues of a membrane.Keywords
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