(Uniqueness for the Dirichlet problem) The Dirichlet problem
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(Uniqueness for the Dirichlet problem) The Dirichlet problem for the Laplacian operator is the boundary-value problem (
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(Uniqueness for the Dirichlet problem) The Dirichlet problem for the Laplacian operator is the boundary-value problem ( r 2u.x; y; z/ D f .x; y; z/ on D u.x; y; z/ D g.x; y; z/ on S; where f and g are given functions defined on D and S, respectively. Show that this problem can have at most one solution u.x; y; z/. Hint: Suppose there are two solutions, u and v, and apply Exercise 24 to their difference D u ? v.
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