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Elliptic boundary value problem

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Uxx means second derivative with respect to x
Uyy means second derivative with respect to y

Uxx + Uyy = 0, 0 < x < pi, 0 < y < pi

U(x,0) = 0, U(x,pi) = 1, 0 < x < pi

U(0,y) = 0, U(pi,y) = 1 0 < y < pi

I know the problem has to be broken into 2 separate problems using U = V + W with zero conditions on 3 sides for each problem W and V. So please show the problem in this manner. Please show all work including the derivation of any eigenvalues or eigenvectors.

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Solution Summary

The solution shows to solve an elliptic boundary value problem.

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