Large m asymptotics for minimal partitions of the Dirichlet eigenvalue

作     者：Zhiyuan Geng Fanghua Lin Zhiyuan Geng;Fanghua Lin

作者机构：Courant Institute of Mathematical SciencesNew York UniversityNew YorkNY 10012USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2022年第65卷第1期

页      面：1-8页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Science Foundation of USA(Grant Nos.DMS1501000 and DMS-1955249) 

主　　题：Dirichlet eigenvalue l1 minimal partition problem large m asymptotics 

摘      要：In this paper,we study large m asymptotics of the l 1 minimal m-partition problem for the Dirichlet *** any smooth domainΩ⊂R^(n)such that|Ω|=1,we prove that the limit lim_(m→∞)l^(1)_(m)(Ω)=c 0 exists,and the constant c 0 is independent of the shape ofΩ.Here,l^(1)_(m)(Ω)denotes the minimal value of the normalized sum of the first Laplacian eigenvalues for any m-partition ofΩ.