Geodesic
On the Bethe-Sommerfeld conjecture
Journées équations aux dérivées partielles (2000), article no. 17, 13 p.

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We consider the operator in ℝ d ,d≥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 8l>d+3. Previously the finiteness of the number of gaps was known for 4l>d+1. Various approaches to this problem are discussed.

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     author = {Parnovski, Leonid and Sobolev, Alexander V.},
     title = {On the {Bethe-Sommerfeld} conjecture},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {17},
     pages = {1--13},
     publisher = {Universit\'e de Nantes},
     year = {2000},
     doi = {10.5802/jedp.581},
     mrnumber = {2002i:35137},
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Parnovski, Leonid; Sobolev, Alexander V. On the Bethe-Sommerfeld conjecture. Journées équations aux dérivées partielles (2000), article  no. 17, 13 p.. doi: 10.5802/jedp.581

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