Abstract.

In this paper, a boundary value problem including generalized nonhomogenious Cauchy-Riemann equation with general nonlocal boundary conditions in a bounded planer region with Lyapunov line boundary is investigated. First, some states called compatibility conditions are obtained by making use of the generalized solution of Cauchy-Riemann equation. Then, the second kind of Fredholm integral equation for boundary values of the unknown of the main problem is resulted by applying and giving boundary condition. Finally, the singularities in integral kernels are removed or reduced to weak singularities by making use of the proposed method in this paper.

Keywords:

boundary value problem, generalized Cauchy-Riemann equation, compatibility conditions, Fredholm integral equation, regularization, weak singularities.