Generalized Solutions of Nonlocal Elliptic Problems
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- Gurevich, P.L. Math Notes (2005) 77: 614. doi:10.1007/s11006-005-0063-6
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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.