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| Extremum Problems of Laplacian Eigenvalues and Generalized Polya Conjecture |
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Citation： |
Fanghua LIN.Extremum Problems of Laplacian Eigenvalues and Generalized Polya Conjecture[J].Chinese Annals of Mathematics B,2017,38(2):497~512 |
| Page view： 756
Net amount： 548 |
Authors： |
Fanghua LIN; |
Foundation： |
This work was supported by the NSF Grant DMS-1501000. |
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| Abstract： |
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. |
Keywords： |
Extremum problems, Laplacian eigenvalues, Weyl asymptotics, Polya'sconjecture, Spliting equality, Regularity of minimizers |
Classification： |
35, 49, 57 |
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