A Priori Estimate of Solutions of One Boundary-Value Problem in a Strip for a Higher-Order Degenerate Elliptic Equation.

In this paper, we prove coercive a priori estimates of solutions of a Dirichlet-type boundary-value problem in a strip for a certain higher-order degenerate elliptic equation containing weighted derivatives of a special form up to the order 2m and ordinary partial derivatives up to the order 2k−1 under the condition 2m > 2k −1. At the boundary of the strip, Dirichlet-type conditions are imposed. A coercive a priori estimate for solutions of the problem considered in special weighted Sobolev-type spaces is obtained. [ABSTRACT FROM AUTHOR]