Show that there is only one function u which takes given values on the (closed) boundary
Chapter 13, Problem 16(choose chapter or problem)
Show that there is only one function u which takes given values on the (closed) boundary of a region and satisfies Laplaces equation 2u = 0 in the interior of the region. Hints: Suppose u1 and u2 are both solutions with the same boundary conditions so that U = u1 u2 = 0 on the boundary. In Greens first identity (Chapter 6, 10.16), let == U to show that U 0. Thus show U 0 everywhere inside the region.
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