Extremum Problems of Laplacian Eigenvalues and Generalized Polya Conjecture(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)  

作　　者：Fanghua LIN 

机构地区：[1]courant institute of mathematical sciences,251 Mercer Street,New York,NY.10012,USA.

出　　处：《Chinese Annals of Mathematics,Series B》2017年第2期497-512,共16页数学年刊（B辑英文版）

基　　金：supported by the NSF Grant DMS-1501000

摘　　要：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.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.

关 键 词：Extremum problems  Laplacian eigenvalues  WEYL asymptotics  Polya'sconjecture  Spliting equality  Regularity of MINIMIZERS 

分 类 号：O175[理学—数学]