Large m asymptotics for minimal partitions of the Dirichlet eigenvalue

Zhiyuan Geng; Fanghua Lin

doi:10.1007/s11425-020-1802-6

Large m asymptotics for minimal partitions of the Dirichlet eigenvalue

Zhiyuan Geng, Fanghua Lin

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Journal	Science China Mathematics
Volume	65
Issue number	1
DOIs	https://doi.org/10.1007/s11425-020-1802-6
State	Published - Jan 2022

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.1007/s11425-020-1802-6

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title = "Large m asymptotics for minimal partitions of the Dirichlet eigenvalue",

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.",

keywords = "35P05, 47A75, 49R05, Dirichlet eigenvalue, l minimal partition problem, large m asymptotics",

author = "Zhiyuan Geng and Fanghua Lin",

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doi = "10.1007/s11425-020-1802-6",

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AU - Lin, Fanghua

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N2 - 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.

AB - 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.

KW - 35P05

KW - 47A75

KW - 49R05

KW - Dirichlet eigenvalue

KW - l minimal partition problem

KW - large m asymptotics

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JO - Science China Mathematics

JF - Science China Mathematics

IS - 1

ER -

Large m asymptotics for minimal partitions of the Dirichlet eigenvalue

Abstract

Keywords

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