Extremum problems of Laplacian eigenvalues and generalized Polya conjecture
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In this survey on extremum problems of Laplacian-Dirichlet eigenvalues of Euclidian domains, the author briefly presents some relevant classical results and recent progress. The main goal is to describe the well-known conjecture due to Polya, its connections to Weyl’s asymptotic formula for eigenvalues and shape optimizations. Many related open problems and some preliminary results are also discussed.
KeywordsExtremum problems Laplacian eigenvalues Weyl asymptotics Polya’s conjecture Spliting equality Regularity of minimizers
2000 MR Subject Classification35 49 57
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