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When one seeks a harmonic function u, i.e., Au = 0 where 0 2 0 2 A denotes the Laplacian operator 0X~l + ... + ~ over some n-dimensional domain ~1, one commonly encounters three boundary conditions. The first is the Dirichlet boundary condition: u(x) = f(x) is given at all x in the boundary 01~. The second is the Nenmann boundary condition: the outward normal derivative Ou/On =fix) is given on 0gl.Then there is a third boundary condition: Ou/On + ~u = f(x) is given on O~, where a is a given positive coefficient. This third boundary condition is variously designated, but frequently it is called Robin's boundary condition. Dirichiet was a prominent mathematician and his contributions to mathematics and science are well known. Less prominent but well known for his contributions to partial differential equations was (Carl) Neumann, for whom the second boundary condition is named.

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