Nodal Domains and Spectral Minimal Partitions

By Bernard Helffer, T. Hoffmann-Ostenhof, S. Terracini. 2006

184 citations recorded by the source corpus.

We consider two-dimensional Schrodinger operators in bounded domains. We analyze relations between the 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 and the characterization of the minimal partitions associated with nodal sets as the nodal domains of Courant-sharp eigenfunctions.

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7b8755d4422b8baf7e165e8ff53f8cc95c331d77

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Bernard Helffer

In Applied Mathematics

1. Bernard Helffer
2. Hugo Tavares
3. S. Terracini
4. Gianmaria Verzini
5. Nicola Soave
6. Nils Berglund

In Geometry and Topology

1. Bernard Helffer
2. S. Terracini

Citations in the corpus

• On Spectral Minimal Partitions: A Survey (2010, methodology): “We will not discuss this point in detail (see [ HHOT1 ]).”
• On hyperboundedness and spectrum of Markov operators (2014, unknown): “[27] (see also the references therein).”
• SIGN-CHANGING SOLUTIONS OF COMPETITION-DIFFUSION ELLIPTIC SYSTEMS AND OPTIMAL PARTITION PROBLEMS (2011, result): “Some preliminary results were also proved by Chang, Lin, Lin and Lin [7] (which, as far as we know, is the first paper to establish a connection between (2) and (4) for ki = 1) and by Conti, Terracini and Verzini [9], while Helffer, Hoffmann-Ostenhof and Terracini [15] have proved that, in dimension”