Algebraic approximations for Laplace’s equation in the neighborhood of interfaces
J. W. Sheldon · Mathematics of Computation · 1958
Problem A:Let d, i = 1, 2, be two simple, closed plane curves with continuous curvature.Let Ci enclose all the points of C\.Let G\ be the region interior to Ci.Let G2 be the region interior to C2 and exterior to &-.Let W be a continuous, bounded function of position on C-l.Let it be required to find harmonic functions F(i) such that (a) F = W on C2.