1. (a) The Green's function G(x, Xo) for the Dirichlet problem for the Laplacian in a domain D is defined by three conditions. What are they? (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? (x, Y, z) such (c) Why does this Green's function satisfy the conditions? (You do not need to verify the conditions in detail. Just give a short reason.)
1. (a) The Green's function G(x, Xo) for the Dirichlet problem for the Laplacian in a domain D is defined by three conditions. What are they? (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? (x, Y, z) such (c) Why does this Green's function satisfy the conditions? (You do not need to verify the conditions in detail. Just give a short reason.)
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Transcribed Image Text:1.
(a) The Green's function G(x, Xo) for the Dirichlet problem for the Laplacian
in 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 to
verify the conditions in detail. Just give a short reason.)
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