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The Y-partition is the optimal three-partition for the disc and the harmonic oscillator
We prove that the Y-partition into three equal sectors is the minimal spectral three-partition both for the Dirichlet Laplacian on the unit disc and for the planar harmonic oscillator $-Δ+|x|^2$, with minimal energies $j_{3/2,1}^{2}$ and $5$; for the disc, this confirms a conjecture of Helffer and H
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