Geodesic
On a magnetic characterization of spectral minimal partitions
Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 2081-2092

Voir la notice de l'article provenant de la source EMS Press

Given a bounded open set Ω in Rn (or in a Riemannian manifold) and a partition of Ω by k open sets Dj​, we consider the quantity maxj​λ(Dj​) where λ(Dj​) is the ground state energy of the Dirichlet realization of the Laplacian in Dj​. If we denote by Lk​(Ω) the infimum over all the k-partitions of maxj​λ(Dj​), a minimal k-partition is then a partition which realizes the infimum. When k=2, we find the two nodal domains of a second eigenfunction, but the analysis of higher k's is non trivial and quite interesting. In this paper, we give the proof of one conjecture formulated in [5] and [16] about a magnetic characterization of the minimal partitions when n=2.
DOI : 10.4171/jems/415
Classification : 35-XX
Keywords: minimal partitions, nodal sets, Aharonov-Bohm Hamiltonians, Courant's nodal theorem 
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Bernard Helffer; Thomas Hoffmann-Ostenhof. On a magnetic characterization of spectral minimal partitions. Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 2081-2092. doi: 10.4171/jems/415

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