Greens Functions and Boundary Value Problems
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Date
2014-08
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Addis Ababa University
Abstract
In this paper, we investigate some boundary value problems for two dimensional harmonic
functions. That is basic introduce new tools for solving Dirichlet problems, Poisson’s equations
and Neumann problems with Green’s function
G( x; y; x0 y0) =1/2in( x –y0)2+( x – y0)2) + h (x ,y, x,0 y0)
Where h is harmonic on the region and
h(x, y, x0 , y0 ) =-1/2in ( x – x0)2 + y - y 0)2)on the boundary .
Roughly speaking Green’s function for a given region Ω and that can be used to solve any
Dirichlet problems or Poisson problems on Ω. In the same way that the Poisson’s kernel on the
real line can be used to solve Dirichlet problems in the upper half plane
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Greens Functions and Boundary Value Problems