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Extremal Problems for Eigenvalue Functionals

โœ Scribed by Barnes, David C.


Book ID
118202956
Publisher
Society for Industrial and Applied Mathematics
Year
1985
Tongue
English
Weight
947 KB
Volume
16
Category
Article
ISSN
0036-1410

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Each eigenvalue of the Laplacian, subject to Dirichlet boundary conditions, is shown to attain its extremes over those open planar starlike sets that simultaneously (i) contain a given disk, (ii) occupy a given area, and (iii) do not exceed a prescribed perimeter. Over that subclass of starlike sets