Bounds for the first eigenvalue of the elastically supported membrane on convex domains

Barta's principle and gradient bounds for the torsion function are the main tools for deriving lower bounds for the first eigenvalue. The optimal domains are an infinite strip, a disk or an annulus in different situations.

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2003-09, Vol.54 (5), p.879-902
Main Author: Sperb, R.
Format: Article
Language:English
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Summary:Barta's principle and gradient bounds for the torsion function are the main tools for deriving lower bounds for the first eigenvalue. The optimal domains are an infinite strip, a disk or an annulus in different situations.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-003-3212-3