Complex Analysis: Theory and Applications · Problem 10.2.2

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 sector

0 < \operatorname{Arg}(z) < \frac{\pi}{3}

and has the boundary values

\phi(x,y) = 2 \text{ for } \operatorname{Arg}(z) = \frac{\pi}{3}, \quad \text{and} \quad \phi(x,0) = 1 \text{ for } x > 0.