Geodesic
Nodal domain theorems à la Courant
Documenta mathematica, Tome 9 (2004), pp. 283-299
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

Let H(Ω0​)=−Δ+V be a Schrödinger operator on a bounded domain Ω0​⊂Rd(d≥2) with Dirichlet boundary condition. Suppose that Ωl​(l∈{1,...,k}) are some pairwise disjoint subsets of Ω0​ and that H(Ωl​) are the corresponding Schrödinger operators again with Dirichlet boundary condition. We investigate the relations between the spectrum of H(Ω0​) and the spectra of the H(Ωl​). In particular, we derive some inequalities for the associated spectral counting functions which can be interpreted as generalizations of Courant's nodal theorem. For the case where equality is achieved we prove converse results. In particular, we use potential theoretic methods to relate the Ωl​ to the nodal domains of some eigenfunction of H(Ω0​).
DOI : 10.4171/dm/168
Classification : 35B05 
@article{10_4171_dm_168,
     author = {A. Ancona and B. Helffer and T. Hoffmann-Ostenhof},
     title = {Nodal domain theorems \`a la {Courant}},
     journal = {Documenta mathematica},
     pages = {283--299},
     year = {2004},
     volume = {9},
     doi = {10.4171/dm/168},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/168/}
}
TY  - JOUR
AU  - A. Ancona
AU  - B. Helffer
AU  - T. Hoffmann-Ostenhof
TI  - Nodal domain theorems à la Courant
JO  - Documenta mathematica
PY  - 2004
SP  - 283
EP  - 299
VL  - 9
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/168/
DO  - 10.4171/dm/168
ID  - 10_4171_dm_168
ER  - 
%0 Journal Article
%A A. Ancona
%A B. Helffer
%A T. Hoffmann-Ostenhof
%T Nodal domain theorems à la Courant
%J Documenta mathematica
%D 2004
%P 283-299
%V 9
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/168/
%R 10.4171/dm/168
%F 10_4171_dm_168
A. Ancona; B. Helffer; T. Hoffmann-Ostenhof. Nodal domain theorems à la Courant. Documenta mathematica, Tome 9 (2004), pp. 283-299. doi: 10.4171/dm/168

Cité par Sources :