On representation of solutions of second order elliptic systems on the plane

Abstract

The analogue of the Privalov theorem is established for solutions of elliptic systems of second order in Lipshitz domains. The corresponding result is also obtained with respect to the weighted H¨older spaces. The notion of conjugate functions to solutions of elliptic systems is introduced and representations formulas for them are received. For so called strengthen elliptic systems the class of degenerate solutions is described