Ok, so let us suppose that functions u(x,y) and v(x,y) are harmonic in a domain D. Thus uxx+uyy=0, and vxx+vyy=0. In addition, v is a harmonic conjugate to u. Thus ux=vy, and uy=-vx.(adsbygoogle = window.adsbygoogle || []).push({});

*Note ux= partial derivative of u with respect to x, vx=partial derivative of v with respect to x, and so on.

I have to use all of this information to show that functions u and v must be constant throughout domain D.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help me prove that functions u and v must be constant in D

**Physics Forums | Science Articles, Homework Help, Discussion**