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Solving the Poisson Equation on a Surface by Reduction to a 1-Dimensional Problem

Commun. Math. Anal.
Volume 8, Number 1 (2010), 26 - 40

Solving the Poisson Equation on a Surface by Reduction to a 1-Dimensional Problem

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Abstract

We describe a method for solving the Poisson equation on a surface in R3, which, via the introduction of conformal coordinates, reduces the problem to that of solving a system of Fredholm equations of second kind on a union of smooth curves in the plane.