Advanced Engineering Mathematics, 7th Edition

20.5 Poisson Integral Formulas

INTRODUCTION

The success of the conformal mapping method depends on the recognition of the solution to the new Dirichlet problem in the image region R′. It would therefore be helpful if a general solution could be found for Dirichlet problems in either the upper half-plane y ≥ 0 or the unit disk z ≤ 1. The Poisson integral formula for the upper half-plane provides such a solution by expressing the value of a harmonic function u(x, y) at a point in the interior of the upper half-plane in terms of its values on the ...