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