Uniqueness of solutions of boundary value problems for Cauchy- Riemann equation with local and non- local boundary conditions

Abstract

In This paper, we consider two boundary value problems for non homogenuous Cauchy- Riemann equation with local and non-local boundary conditions separatly.In the first problem boundary condition is local and for proving uniqueness of solution, we show that homogenuous boundary value problem has only non-trivial solution. In the second problem, the boundary condition is non-local. At first, the given problem changed to a second kind system of Fredholm integral equation. Then the singularities in the Kernels of integral equations are removed. Finaly, for the uniqueness of solution, we show that the regularized kernels satify in contraction mapping theorem. ./files/site1/files/%D8%B9%D8%A8%D8%A7%D8%AF%D9%BE%D9%88%D8%B1.pdf

Keywords

• cauchy- riemann equation
• uniqueness of solution
• fundamental solution
• regularization
• system of fredholm integral equations