Mathematical Notes

, Volume 77, Issue 5–6, pp 614–629 | Cite as

Generalized Solutions of Nonlocal Elliptic Problems

  • P. L. Gurevich


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 2 m (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 W 2 m (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 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

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

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