Boundary Integral Equations for the Laplace-Beltrami Operator

Abstract

We present a boundary integral method, and an accompanying boundary element discretization, for solving boundary-value problems for the Laplace-Beltrami operator on the surface of the unit sphere in R3. We consider a closed curve C on S which divides S into two parts S1 and S2. In particular, C = ∂ S1 is the boundary curve of S1. We are interested in solving a boundary value problem for the Laplace-Beltrami operator in 2, with boundary data prescribed on .