A boundary value problem for Bitsadze equation in matrix form

In this work, we investigate the solvability of the problem frac{partial^2w}{partial overlinephi ^2}=f Re{iphi(z)w(z)}=gamma_1(z),Rew_{overlinephi}(z)=gamma_2(z) z in partial D in the unit disk of complex plane. Here f , gamma_1 and gamma_2 are given m times s-complex matrix-valued functions; fin L^{p} (overline{D}), gamma_1, gamma_2 in C(partial D) and phi is a generating solution for Q-holomorphic functions.