Extremum problems of Laplacian eigenvalues and generalized Polya conjecture

Fanghua Lin

doi:10.1007/s11401-017-1080-y

Extremum problems of Laplacian eigenvalues and generalized Polya conjecture

Fanghua Lin

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	497-512
Number of pages	16
Journal	Chinese Annals of Mathematics. Series B
Volume	38
Issue number	2
DOIs	https://doi.org/10.1007/s11401-017-1080-y
State	Published - Mar 1 2017

Keywords

Extremum problems
Laplacian eigenvalues
Polya’s conjecture
Regularity of minimizers
Spliting equality
Weyl asymptotics

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1007/s11401-017-1080-y

Cite this

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title = "Extremum problems of Laplacian eigenvalues and generalized Polya conjecture",

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{\textquoteright}s asymptotic formula for eigenvalues and shape optimizations. Many related open problems and some preliminary results are also discussed.",

keywords = "Extremum problems, Laplacian eigenvalues, Polya{\textquoteright}s conjecture, Regularity of minimizers, Spliting equality, Weyl asymptotics",

author = "Fanghua Lin",

note = "Funding Information: This work was supported by the NSF Grant DMS-1501000. Publisher Copyright: {\textcopyright} 2017, Fudan University and Springer-Verlag Berlin Heidelberg.",

year = "2017",

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doi = "10.1007/s11401-017-1080-y",

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AB - 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.

KW - Extremum problems

KW - Laplacian eigenvalues

KW - Polya’s conjecture

KW - Regularity of minimizers

KW - Spliting equality

KW - Weyl asymptotics

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JF - Chinese Annals of Mathematics. Series B

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ER -

Extremum problems of Laplacian eigenvalues and generalized Polya conjecture

Abstract

Keywords

ASJC Scopus subject areas

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