Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle

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dc.creatorOwen, Mark P.
dc.date1998-03-05
dc.date.accessioned2026-07-07T05:23:59Z
dc.date.available2026-07-07T05:23:59Z
dc.descriptionWe 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.
dc.description27 pages, 4 diagrams, 2 tables
dc.identifierhttps://arxiv.org/abs/math/9803011
dc.identifierhttp://arxiv.org/abs/math/9803011
dc.identifierJournal of Differential Equations. Vol. 136, No. 1, (1997)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76663
dc.subjectSpectral Theory
dc.subjectFunctional Analysis
dc.subject35K25
dc.titleAsymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle
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