Large m asymptotics for minimal partitions of the Dirichlet eigenvalue

• 作者: Zhiyuan Geng Fanghua Lin
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2022,（1）
• 所属期刊栏目: Articles
• 页码范围: 1-8
• 页数: 8页
• 语种: 英文

摘要

In this paper,we study large m asymptotics of the l1 minimal m-partition problem for the Dirichlet eigenvalue.For any smooth domain Ω (C) Rn such that |Ω| =1,we prove that the limit limm→∞ l1m(Ω) =c0 exists,and the constant c0 is independent of the shape of Ω.Here,l1m(Ω) denotes the minimal value of the normalized sum of the first Laplacian eigenvalues for any m-partition of Ω.