A boundary value problem for Bitsadze equation in matrix form

Abstract

In this work, we investigate the solvability of the problem

partial derivative(2)w/partial derivative(phi) over bar (2) = f

Re{i phi(z)w(z)} = gamma(1)(z), Rew((phi) over bar)(z) = gamma(2)(z) z is an element of partial derivative D

in the unit disk of complex plane. Here f, gamma(1) and gamma(2) are given m x s-complex matrix-valued functions; f is an element of L(p)((D) over bar), gamma(1), gamma(2) is an element of C(partial derivative D) and phi is a generating solution for Q-holomorphic functions.