Abstract
Let f(x) be a piecewise continuous and bounded function on the real line R. It is a classical result that the solution to the Dirichlet boundary value problem: in the upper half plane is: We extend the notion of the harmonic function to the space Wecall U(x,y)a harmonic function in an open region of Rn+1, +, if it is an infinitely differentiable at each point of the region and satisfies In this paper we exploit the above definition of harmonic functions to solve the Dirichlet boundary value problem in the space Rn+1,1 with a distributional boundary condition. As it turns out, our solution is quite constructive and its two dimensional case is an extension of the corresponding classical Dirichlet-Boundary-Val ue Problem.
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