Large m asymptotics for minimal partitions of the Dirichlet eigenvalue

Zhiyuan Geng, Fanghua Lin

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study large m asymptotics of the l1 minimal m-partition problem for the Dirichlet eigenvalue. For any smooth domain Ω ⊂ ℝn such that ∣Ω∣ = 1, we prove that the limit limm→∞lm1(Ω)=c0 exists, and the constant c0 is independent of the shape of Ω. Here, lm1(Ω) denotes the minimal value of the normalized sum of the first Laplacian eigenvalues for any m-partition of Ω.

Original languageEnglish (US)
JournalScience China Mathematics
DOIs
StateAccepted/In press - 2021

Keywords

  • 35P05
  • 47A75
  • 49R05
  • Dirichlet eigenvalue
  • l minimal partition problem
  • large m asymptotics

ASJC Scopus subject areas

  • Mathematics(all)

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