Complex Analysis: Theory and Applications · Problem 10.2.1

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 horizontal strip

1 < \operatorname{Im}(z) < 2

and has the boundary values

\phi(x,1) = 6 \text{ for all } x, \quad \text{and} \quad \phi(x,2) = -3 \text{ for all } x.