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

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.

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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},
     eid = {17},
     publisher = {Universit\'e de Nantes},
     year = {2000},
     zbl = {01808707},
     mrnumber = {2002i:35137},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_2000____A17_0/}
}
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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. http://www.numdam.org/item/JEDP_2000____A17_0/

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