On elliptic boundary value problems on upper half-plane

The boundary value problems for elliptic systems of the second order with leading and constant coefficients are considered in a half-plane. The investigation is based on the Bitsadze formula which represents a general solution of this system through a vector-valued analytic function. The transformation of this formula is studied in Holder spaces with weight. As a consequence, the explicit formulas of the solution to the problems are received. The applications to anisotropic elasticity are also given.