Geodesic
The solution of the first boundary-value problem for self-adjoint elliptic equations in the case of an unbounded region
Izvestiya. Mathematics , Tome 1 (1967) no. 5, pp. 1131-1151

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In this paper we solve the first boundary-value problem for a self-adjoint second order elliptic equation in the case of an unbounded region in a certain class of functions, which is defined in a natural way by the equation itself. Existence and uniqueness theorem are proved by means of a variational method. 
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     author = {L. D. Kudryavtsev},
     title = {The solution of the first boundary-value problem for self-adjoint elliptic equations in the case of an unbounded region},
     journal = {Izvestiya. Mathematics },
     pages = {1131--1151},
     publisher = {mathdoc},
     volume = {1},
     number = {5},
     year = {1967},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_5_a12/}
}
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L. D. Kudryavtsev. The solution of the first boundary-value problem for self-adjoint elliptic equations in the case of an unbounded region. Izvestiya. Mathematics , Tome 1 (1967) no. 5, pp. 1131-1151. http://geodesic.mathdoc.fr/item/IM2_1967_1_5_a12/