On the Existence of Solutions to a Class of Boundary Value Problems in a Strip for High-Order Degenerate Elliptic Equations

Abstract—Problems in a strip for high-order elliptic equations that degenerate into an odd-order equation on the strip boundary are studied. Coercive a priori estimates and existence and uniqueness theorems for solutions of such problems are obtained in special weighted Sobolev-type spaces. The norms in these spaces are defined with the help of a special integral transform.