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Unformatted text preview: Thus, assume that D is an open and bounded subset of R n with boundary D . Assume also that u ( x ) is a solution to Laplaces equation u = 0 in D and that u is continuous on D , twice dierentiable in D . Show that sup D u = sup D u 5. a. Prove that if there exists a solution of the Neumann problem u = f for x D R n , u n = h ( x ) for x D, then it is unique up to adding an arbitrary constant. b. Consider the Robin problem u = f for x D , u n + a ( x ) u = h ( x ) for x D Show that its solutions are unique. 1...
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- Spring '08