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|
|State||Published - Jan 2022|
- Dirichlet eigenvalue
- l minimal partition problem
- large m asymptotics
ASJC Scopus subject areas