JournalsaihpcVol. 26, No. 1pp. 101–138

Nodal domains and spectral minimal partitions

  • S. Terracini

    Università di Milano Bicocca, Via Cozzi, 53, 20125 Milano, Italy

  • B. Helffer

    Département de Mathématiques, Bat. 425, Université Paris-Sud, 91405 Orsay Cedex, France

  • T. Hoffmann-Ostenhof

    Institut für Theoretische Chemie, Universität Wien, Währinger Strasse 17, A-1090 Wien, Austria, International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, A-1090 Wien, Austria
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Abstract

We consider two-dimensional Schrödinger operators in bounded domains. We analyze relations between the nodal domains of eigenfunctions, spectral minimal partitions and spectral properties of the corresponding operator. The main results concern the existence and regularity of the minimal partitions and the characterization of the minimal partitions associated with nodal sets as the nodal domains of Courant-sharp eigenfunctions.

Cite this article

S. Terracini, B. Helffer, T. Hoffmann-Ostenhof, Nodal domains and spectral minimal partitions. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 1, pp. 101–138

DOI 10.1016/J.ANIHPC.2007.07.004