Abstract
Galerkin method for an integral equation on a boundary δΩ of a bounded domain in R2, arising from a Dirichlet boundary value problem for an elliptic partial differential equation is considered in this paper. By using a single layer potential corresponding to the problem we obtain an integral equation on the boundary. The main result of the paper is that the integral equation has a unique solution in the Sobolev space H-1/2 (δΩ). We also give its H1 (Ω)-error estimate.
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