On Degenerate Elliptic Equations of High Order and Pseudodifferential Operators with Degeneration

Abstract—Problems for high-order degenerate elliptic equations in a half-space are studied. Coercive a priori estimates and existence theorems for solutions of such problems in special weighted Sobolev-type spaces are obtained. The norms in these spaces are defined with the help of a special integral transform. Pseudodifferential operators with degeneration constructed using a special integral transform are studied. Pseudodifferential operators with degeneration are used to factorize the symbol of a high-order degenerate elliptic operator and to construct a separating operator of the Leray–Sakamoto type.