Generalized Dirichlet problem for elliptic equation degenerating on unbounded manifolds

In the paper we investigate the unique solvability of a generalized Dirichlet problem for higher order elliptic equation, degenerating on unbounded $C^0$ — manifolds of arbitrary dimension less then dimension of the space. Differential properties of the solution are studied depending on the smoothness of coefficients of the differential operator, the right-hand side of differential equation and boundary functions.
The method applied in the paper is based on elements of the embedding theory weighted function spaces. Therefore in the paper first necessary imbedding theorems for the corresponding function spaces are established.