Mathematical Notes

, Volume 77, Issue 5–6, pp 614–629

Generalized Solutions of Nonlocal Elliptic Problems

  • P. L. Gurevich

DOI: 10.1007/s11006-005-0063-6

Cite this article as:
Gurevich, P.L. Math Notes (2005) 77: 614. doi:10.1007/s11006-005-0063-6


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 W2m (G) are studied. The Fredholm property of the unbounded operator (corresponding to the elliptic equation) acting on L2(G), and defined for functions from the space W2m (G) that satisfy homogeneous nonlocal conditions, is established.

Key words

nonlocal elliptic problem Sobolev space Fredholm property properly elliptic operator generalized solution (distribution) Lopatinsky condition 

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • P. L. Gurevich
    • 1
  1. 1.Moscow Aviation InstituteMoscowRussia

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