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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
