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Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle

✍ Scribed by M.P. Owen

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 380 KB
Volume: 136
Category: Article
ISSN: 0022-0396
DOI: 10.1006/jdeq.1996.3235

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✦ Synopsis

We find an asymptotic expression for the first eigenvalue of the biharmonic operator on a long thin rectangle. This is done by finding lower and upper bounds which become increasingly accurate with increasing length. The lower bound is found by algebraic manipulation of the operator, and the upper bound is found by minimising the quadratic form for the operator over a test space consisting of separable functions. These bounds can be used to show that the negative part of the groundstate is small.

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