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

Ebadpur Golanbar, Javad; Jahanshahi, Mohammad; Aliyev, Nihan

Volume 7, Issue 4 (Vol. 7,No. 4, 2021) mmr 2021, 7(4): 843-857 | Back to browse issues page

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Ebadpur Golanbar J, Jahanshahi M, Aliyev N. Uniqueness of solutions of boundary value problems for Cauchy- Riemann equation with local and non- local boundary conditions. mmr 2021; 7 (4) :843-857
URL: http://mmr.khu.ac.ir/article-1-2858-en.html

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

Javad Ebadpur Golanbar

, Mohammad Jahanshahi

¹, Nihan Aliyev

1- , jahanshahi@azaruniv.ac.ir

Abstract: (873 Views)

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.

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Keywords: Cauchy- Riemann equation, uniqueness of solution, Fundamental solution, regularization, system of Fredholm integral equations

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