Nodal domains and spectral minimal partitions
Seminar Room 1, Newton Institute
Abstract: We consiser two-dimensional Schr\"odinger operators in bounded domains. We analyze relations between the nodal domains of eigengunctions, 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 for the case that in Courant's nodal theorem there is equality.