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Large $m$ asymptotics for minimal partitions of the Dirichlet eigenvalue
- Publication Year :
- 2020
-
Abstract
- In this paper, we study large $m$ asymptotics of the $l^1$ minimal $m$-partition problem for Dirichlet eigenvalue. For any smooth domain $\Omega\in \mathbb{R}^n$ such that $|\Omega|=1$, we prove that the limit $\lim\limits_{m\rightarrow\infty}l_m^1(\Omega)=c_0$ exists, and the constant $c_0$ is independent of the shape of $\Omega$. Here $l_m^1(\Omega)$ denotes the minimal value of the normalized sum of the first Laplacian eigenvalues for any $m$-partition of $\Omega$.<br />Comment: This paper has been accepted for publication in SCIENCE CHINA Mathematics
- Subjects :
- Mathematics::Functional Analysis
General Mathematics
010102 general mathematics
Mathematics::Spectral Theory
01 natural sciences
Omega
Laplacian eigenvalues
Combinatorics
Dirichlet eigenvalue
Mathematics - Analysis of PDEs
0103 physical sciences
Domain (ring theory)
FOS: Mathematics
010307 mathematical physics
Limit (mathematics)
0101 mathematics
Constant (mathematics)
Analysis of PDEs (math.AP)
Mathematics
49R05, 35P05, 47A75
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....3f59ac8844bd3f397c0f452cf264cee7