= 1 8.5 (a) Let x = (x1, x2, x3) and consider the function defined for...

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= 1 8.5 (a) Let x = (x1, x2, x3) and consider the function defined for x = 0, u(x) Show by direct differentiation that for x 0, Au(x) = 0. Thus, u is a radially symmetric harmonic function away from the origin. (b) Now consider the same function in 2D. Show that for x 0, Au(x) = 0. = 1 8.5 (a) Let x = (x1, x2, x3) and consider the function defined for x = 0, u(x) Show by direct differentiation that for x 0, Au(x) = 0. Thus, u is a radially symmetric harmonic function away from the origin. (b) Now consider the same function in 2D. Show that for x 0, Au(x) = 0.

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a To show that Aux 0 for x 0 where ux x we need to compute the Laplacian of u and show that it is eq... View the full answer