We consider two-dimensional Schr¨odinger operators in bounded domains. We analyze relations between the nodal domains, 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.

Helffer, B., Hoffmann Ostenhof, T., Terracini, S. (2009). Nodal domains and spectral minimal partitions. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 26(1), 101-138 [10.1016/j.anihpc.2007.07.004].

Nodal domains and spectral minimal partitions

TERRACINI, SUSANNA
2009

Abstract

We consider two-dimensional Schr¨odinger operators in bounded domains. We analyze relations between the nodal domains, 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.
Articolo in rivista - Articolo scientifico
spectral theory, schroedinger operator, nodal partitions
English
2009
26
1
101
138
none
Helffer, B., Hoffmann Ostenhof, T., Terracini, S. (2009). Nodal domains and spectral minimal partitions. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 26(1), 101-138 [10.1016/j.anihpc.2007.07.004].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/5324
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