A priori estimate of solutions of one boundary-value problem in a strip for a higher-order degenerate elliptic equation

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 $2m>2k-1$ are proved. 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.