Dirichlet type problem for the system of elliptic equations, which order degenerate at a line

Dirichlet type problem in a bounded domain for the system of linear elliptic equations of second order, which degenerate into first order system at a line crossing the domain, is studied. The existence and uniqueness of a solution of this problem in the Holder class of functions are proved without any additional condition at line of degeneracy. The only requirement is that the solution is bounded in the considered domain.