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Journal of Siberian Federal University. Mathematics & Physics, 2008, Volume 1, Issue 2, Pages 158–187 (Mi jsfu17)  

Boundary Value Problems with Non-Local Conditions

Nikolai N. Tarkhanov

Universität Potsdam, Institut für Mathematik, Potsdam, Germany
References:
Abstract: We describe a new algebra of boundary value problems which contains Lopatinskii elliptic as well as Toeplitz type conditions. These latter are necessary, if an analogue of the Atiyah–Bott obstruction does not vanish. Every elliptic operator is proved to admit up to a stabilisation elliptic conditions of such a kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. The crucial novelty consists of the new type of weighted Sobolev spaces which fit well to the nature of pseudodifferential operators.
Keywords: pseudodifferential operators, boundary values problems, Toeplitz operators.
Received: 11.01.2008
Received in revised form: 20.02.2008
Accepted: 05.03.2008
UDC: 517.55
Language: English
Citation: Nikolai N. Tarkhanov, “Boundary Value Problems with Non-Local Conditions”, J. Sib. Fed. Univ. Math. Phys., 1:2 (2008), 158–187
Citation in format AMSBIB
\Bibitem{Tar08}
\by Nikolai~N.~Tarkhanov
\paper Boundary Value Problems with Non-Local Conditions
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2008
\vol 1
\issue 2
\pages 158--187
\mathnet{http://mi.mathnet.ru/jsfu17}
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    Журнал Сибирского федерального университета. Серия "Математика и физика"
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