Biharmonic green function of a ring domain

Abstract

A biharmonic Green function of a circular ring domain R = {z * C : 0 < r < |z| < 1} is found in the form Ĝ2(z, ζ) = |ζ - z|2G1(z, ζ ) +ĥ2(z, ζ ), whereG1(z, ζ ) is the harmonic Green function of the ringR, and ĥ2(z, ζ ) is a specially constructed biharmonic function.