Fulfillment of boundary conditions in the differential factorization method

The fulfillment of the boundary conditions by differential factorization method is discussed. It was assumed that the body under study is convex and has a smooth boundary with a twice continuously differentiated curvature. A well-known technique of coordinate axes stretching in the neighborhood of the boundary point is used and its application reveal that the problem is reduced to the study of the fulfillment of boundary conditions for a half-space. In the case of a half-space or a layered medium, pseudodifferential equations degenerate into algebraic ones. Since the differential factorization method can be applied in the same manner to a system or a single equation, for brevity the boundary value problem for a single finite-order differential equation is also considered.