Let f = u + iv be holomorphic on Ω and let h(u, v) be a harmonic function of u and v on f(Ω). Prove that g(x, y) = h (u(x, y), v(x, y)) defines a harmonic function on Ω.
Added by Rachel G.
Step 1
Since f is holomorphic on Ω, it satisfies the Cauchy-Riemann equations: \(\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}\) and \(\frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x}\) Show more…
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