Extremals for Eigenvalues of Laplacians
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Richard Snyder Laugesen; Carlo Morpurgo
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Article
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1998
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Elsevier Science
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English
β 441 KB
Po lya and G. Szego showed in 1951 that for simply connected plane domains, the first eigenvalue of the Laplacian (with Dirichlet boundary conditions) is maximal for a disk, under a conformal mapping normalization. That is, if f (z) is a conformal map of a disk D onto a bounded, simply connected pla