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

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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:   (2054 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
Full-Text [PDF 568 kb]   (594 Downloads)    
Type of Study: S | Subject: alg
Received: 2018/10/17 | Revised: 2022/11/15 | Accepted: 2020/05/11 | Published: 2022/03/29 | ePublished: 2022/03/29
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