Boundary value problems for a system of first order equations of a principal type in the plane

The author gives a concise summary of research results concerning the boundary value problem Cu=f on Gamma=partialscr D for the system of composite type partial u/partial x_2=apartial u/partial x_1 with constant real coefficients, where C is a matrix-valued function, and f is a vector-valued function. Sufficient conditions for the problem to be Noetherian and a formula for the index are obtained. par The case when the boundary partialscr D of the infinite domain scr D consists of two smooth curves Gamma_1 and Gamma_2 that connect two corner points is considered analogously. The functions satisfy a Hölder condition with weights.