Mathematics – Analysis of PDEs
Scientific paper
2009-02-23
Mathematics
Analysis of PDEs
32 pages
Scientific paper
In this paper we consider a stationary Schroedinger operator in the plane, in presence of a magnetic field of Aharonov-Bohm type with semi-integer circulation. We analyze the nodal regions for a class of solutions such that the nodal set consists of regular arcs, connecting the singular points with the boundary. In case of one magnetic pole, which is free to move in the domain, the nodal lines may cluster dissecting the domain in three parts. Our main result states that the magnetic energy is critical (with respect to the magnetic pole) if and only if such a configuration occurs. Moreover the nodal regions form a minimal 3-partition of the domain (with respect to the real energy associated to the equation), the configuration is unique and depends continuously on the data. The analysis performed is related to the notion of spectral minimal partition introduced in [20]. As it concerns eigenfunctions, we similarly show that critical points of the Rayleigh quotient correspond to multiple clustering of the nodal lines.
Noris Benedetta
Terracini Susanna
No associations
LandOfFree
Nodal sets of magnetic Schroedinger operators of Aharonov-Bohm type and energy minimizing partitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nodal sets of magnetic Schroedinger operators of Aharonov-Bohm type and energy minimizing partitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nodal sets of magnetic Schroedinger operators of Aharonov-Bohm type and energy minimizing partitions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-584773