Extremals for Eigenvalues of Laplacians
โ
Richard Snyder Laugesen; Carlo Morpurgo
๐
Article
๐
1998
๐
Elsevier Science
๐
English
โ 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