General boundary value problem for systems elliptic in the sense of Douglis–Nirenberg in domains with smooth boundary

A study is made of a general boundary value problem for systems elliptic in the Douglis–Nirenberg sense with constant real coefficients in domains with smooth boundary. A representation is obtained for regular solutions of these systems by means of solutions of (canonical) elliptic systems, and a formula is given for the index of the problem. Certain boundary value problems for the Stokes system are studied as an illustration.