Abstract
An elliptic equation of order 2m with general nonlocal boundary-value conditions, in a plane bounded domain G with piecewise smooth boundary, is considered. Generalized solutions belonging to the Sobolev space W m2 (G) are studied. The Fredholm property of the unbounded operator (corresponding to the elliptic equation) acting on L 2(G), and defined for functions from the space W m2 (G) that satisfy homogeneous nonlocal conditions, is established.
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Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 665–682.
Original Russian Text Copyright ©2005 by P. L. Gurevich.
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Gurevich, P.L. Generalized Solutions of Nonlocal Elliptic Problems. Math Notes 77, 614–629 (2005). https://doi.org/10.1007/s11006-005-0063-6
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DOI: https://doi.org/10.1007/s11006-005-0063-6