Generalized Solutions of Nonlocal Elliptic Problems

P. L. Gurevich

Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 665-682.

Résumé

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 $L_2(G)$, and defined for functions from the space $W_2^m(G)$ that satisfy homogeneous nonlocal conditions, is established.

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