Mathematics – Spectral Theory
Scientific paper
2006-10-31
Mathematics
Spectral Theory
Scientific paper
We consider two-dimensional Schr\"odinger operators in bounded domains. We analyze relations between 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 associated with the nodal sets as the nodal domains of Courant-sharp eigenfunctions.
Helffer Bernard
Hoffmann-Ostenhof Thomas
Terracini Susanna
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