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

摘要

In this paper we consider two boundary-value problems in a band for higher-order degenerate elliptic equations. These equations degenerate on one boundary of the band to a thirdorder equation with respect to one variable. We study problems in weight spaces similar to Sobolev ones whose norms are constructed with the help of a certain integral transform. We obtain a priori estimates in these weight spaces for solutions to boundary-value problems in the band for higherorder elliptic equations that degenerate on one boundary of the band to a third-order equation with respect to one variable.