On the Bethe-Sommerfeld conjecture
Parnovski, Leonid ; Sobolev, Alexander V.
Journées équations aux dérivées partielles, (2000), p. 1-13 / Harvested from Numdam

We consider the operator in d ,d2, of the form H=(-Δ) l +V,l>0 with a function V periodic with respect to a lattice in d . We prove that the number of gaps in the spectrum of H is finite if 8l>d+3. Previously the finiteness of the number of gaps was known for 4l>d+1. Various approaches to this problem are discussed.

Publié le : 2000-01-01
@article{JEDP_2000____A17_0,
     author = {Parnovski, Leonid and Sobolev, Alexander V.},
     title = {On the Bethe-Sommerfeld conjecture},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2000},
     pages = {1-13},
     mrnumber = {2002i:35137},
     zbl = {01808707},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2000____A17_0}
}
Parnovski, Leonid; Sobolev, Alexander V. On the Bethe-Sommerfeld conjecture. Journées équations aux dérivées partielles,  (2000), pp. 1-13. http://gdmltest.u-ga.fr/item/JEDP_2000____A17_0/

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