A priori estimates of solutions of boundary value problems in a band for a class of degenerate elliptic equation of higher order

In this paper we consider two boundary value problems in a band for degenerate elliptic equations of higher order. These equations degenerate on one boundary of a band into the third-order equation in one variable. Problems are investigated in weight spaces, similar to weight Sobolev spaces, which norms are built using a special integral transform. We obtain a priori estimates in weight spaces of solutions of boundary value problems in a band for higher order elliptic equations degenerating at one boundary of a band into the third-order equation in one variable.