Elliptic equations in unbounded domains

A linear differential operator in $\mathbf R^n$ of elliptic type, with varying coefficients, is considered along with a boundary value problem for such an operator in the exterior of a bounded region. Certain conditions on the symbol of the operator are assumed, the formulation of which involves lower-order terms. The study is carried out in Sobolev spaces with weighting. The weighting is constructed with respect to the coefficients of the equation. The coefficients of the operator may be unbounded at infinity.
The principal result is the proof that the operator and corresponding boundary value problem are Noetherian.
Bibliography: 10 titles.