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 \({\rm{lim}}_{m \to \infty}l_m^1\left(\Omega \right) = {c_0}\) exists, and the constant c0 is independent of the shape of Ω. Here, \(l_m^1\left({\rm{\Omega}} \right)\) denotes the minimal value of the normalized sum of the first Laplacian eigenvalues for any m-partition of Ω.
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Acknowledgements
This work was supported by National Science Foundation of USA (Grant Nos. DMS-1501000 and DMS-1955249).
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Geng, Z., Lin, F. Large m asymptotics for minimal partitions of the Dirichlet eigenvalue. Sci. China Math. 65, 1–8 (2022). https://doi.org/10.1007/s11425-020-1802-6
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DOI: https://doi.org/10.1007/s11425-020-1802-6