If $$f(z)=u(x,y)+iv(x,y)$$ is analytic in a domain D, then both u and v satisfy Laplace's equations(adsbygoogle = window.adsbygoogle || []).push({});

$$\nabla^2 u=u_{xx} + u_{yy}=0$$

$$\nabla^2 v=v_{xx} + v_{yy}=0$$

and u and v are called harmonic functions.

My question is whether or not this goes both ways. If you have two functions u and v which satisfy the Laplace equations are they the real and imaginary parts of an analytic function?

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# Harmonic functions

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