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In this paper we compare the candidates to be spectral minimal partitions fortwo criteria: the maximum and the average of the first eigenvalue on eachsubdomains of the partition. We analyze in detail the square, the disk and theequilateral triangle. Using numerical simulations, we propose candidates forthe max, prove that most of them can not be optimal for the sum and thenexhibit better candidates for the sum.

Optimal partitions for the sum and the maximum of eigenvalues