Abstract:
In this paper we obtain coercive a priori estimates of solutions to the boundary value problem of the Dirichlet type in a strip for a degenerate high-order elliptic equation and prove existence and uniqueness of such solutions. The equation contains weight operators, which are a superposition of the multiplication operator on the function, which vanishes at the boundary, and the differentiation operator. We consider conditions of the Dirichlet type on the strip boundary. We obtain estimates in special weight spaces such as Sobolev spaces.
Keywords:a priori estimate, degenerate elliptical equation, S. L. Sobolev's weight spaces, weight derivatives, existence and uniqueness theorem.
