For harmonic functions $u,v$ from $D \subset \mathbb{C}$ to $\mathbb R$ can we say the following: $ u + v $, $u^2$,$v^2$,$\sqrt{u^2+v^2}$ are also harmonic under the same conditions.
2026-04-05 01:13:15.1775351595
About harmonic functions
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No. Why should that be true? Take $u(x,y)=x^2-y^2$. It is an harmonic function, but $u^2$ is not.