Complex Analysis: Theory and Applications · Problem 10.2.3

Applications of Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · dirichlet-problem-harmonic-functions

Problem

Find the function

\phi(x,y)

that is harmonic in the annulus

1 < |z| < 2

and has the boundary values

\phi(x,y) = 5 \text{ when } |z| = 1, \quad \text{and} \quad \phi(x,y) = 8 \text{ when } |z| = 2.