Greens Functions And Boundary Value Problems

In this paper, we investigate some boundary value problems for two dimensional harmonicrnfunctions. That is basic introduce new tools for solving Dirichlet problems, Poisson’s equationsrnand Neumann problems with Green’s functionrnG( x; y; x0 y0) =1/2in( x –y0)2+( x – y0)2) + h (x ,y, x,0 y0)rnWhere h is harmonic on the region andrnh(x, y, x0 , y0 ) =-1/2in ( x – x0)2 + y - y 0)2)on the boundary  .rnRoughly speaking Green’s function for a given region Ω and that can be used to solve anyrnDirichlet problems or Poisson problems on Ω. In the same way that the Poisson’s kernel on thernreal line can be used to solve Dirichlet problems in the upper half plane

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