1.(a) The Green's function G(x, Xo) for the Dirichlet problem for the Laplacianin a domain D is defined by three conditions. What are they?(x, y, z) such(b) Suppose the region D is the half space consisting of all x =that z > 0. What is the Green's function in this case?(c) Why does this Green's function satisfy the conditions? (You do not need toverify the conditions in detail. Just give a short reason.)

To answer: (a) The Green's function G(x,x0) for the Dirichlet problem for the Laplacian in domain D…

Answered: 1. (a) The Green's function G(x, Xo)…

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