Summary: The Neumann problem is investigated for a selfadjoint, elliptic (in the Douglis-Nirenberg sense) system in an n-dimensional domain, whose boundary contains a d-dimensional edge. Noether type theorems are proved for the operator of the boundary value problem in functional spaces in which the norms contain as weight multipliers the powers of the distance to the edge. Under certain relations, connecting the dimensions n, d, and the orders of the differential operators occurring in the system, the mentioned space must necessarily have a nonhomogeneous (noninvariant with respect to extensions) norm.