Degenerating elliptic differential and psevdo-differential operators

The present paper is a survey of some results concerning higher-order elliptic differential operators which degenerate on the boundary of a domain. The principal aspect in the study of such operators is that of investigating the corresponding ordinary equations with parameters which degenerate at a single point. The parametrix for such operators is a degenerating pseudo-differential operator. We investigate the properties of the kernels of these pseudo-differential operators.