ON A CLASS OF ELLIPTIC PSEUDODIFFERENTIAL OPERATORS DEGENERATE ON A SUBMANIFOLD

Abstract

There are investigated elliptic pseudodifferential operators p(x, D) which are degenerate on a submanifold Γ of any codimension. Under certain further assumptions, for the operator which is obtained by adjoining to p(x, D) boundary and coboundary conditions on the submanifold Γ, there are constructed left and right regularizers, and theorems on hypoellipticity and local solvability are proved. In case p(x, D) is defined on a smooth compact manifold it is shown to be noetherian on special weighted spaces of Sobolev type. Bibliography: 24 references.