Abstract
This article studies pseudodifferential operators which are elliptic outside an (n - 1)-dimensional submanifold ω of a closed n-dimensional manifold Γ. It is assumed that at those points of the cotangent bundle at which the ellipticity condition is violated the gradient of the determinant of the symbol is nonzero and transversal to ω. On ω a number of boundary conditions are prescribed, and a number of potential operators with unknown densities are adjoined to the original equation; the normal solvability of this boundary value problem is then established. Bibliography: 21 items.