On a magnetic characterization of spectral minimal partitions

  • Bernard Helffer

    Université de Nantes, France
  • Thomas Hoffmann-Ostenhof

    Universität Wien, Austria


Given a bounded open set in (or in a Riemannian manifold) and a partition of by open sets , we consider the quantity where is the ground state energy of the Dirichlet realization of the Laplacian in . If we denote by the infimum over all the -partitions of , a minimal -partition is then a partition which realizes the infimum. When , we find the two nodal domains of a second eigenfunction, but the analysis of higher '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 .

Cite this article

Bernard Helffer, Thomas Hoffmann-Ostenhof, On a magnetic characterization of spectral minimal partitions. J. Eur. Math. Soc. 15 (2013), no. 6, pp. 2081–2092

DOI 10.4171/JEMS/415