On the Bethe-Sommerfeld conjecture

Parnovski, Leonid; Sobolev, Alexander V.

Parnovski, Leonid ; Sobolev, Alexander V.

Journées équations aux dérivées partielles, (2000), p. 1-13 / Harvested from Numdam

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Résumé

We consider the operator in $ℝ^{d}, d \geq 2$ , of the form $H = {(- Δ)}^{l} + V, l > 0$ with a function $V$ periodic with respect to a lattice in $ℝ^{d}$ . We prove that the number of gaps in the spectrum of $H$ is finite if $8 l > d + 3$ . Previously the finiteness of the number of gaps was known for $4 l > d + 1$ . Various approaches to this problem are discussed.

Publié le : 2000-01-01

MR 2002i:35137 | Zbl 01808707

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     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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