Local harmonic conjugate
= Local harmonic conjugate
On a disc, the closed one-form $-u_y\,dx+u_x\,dy$ has a potential $v$ when $\Delta u=0$. The Cauchy--Riemann equations then make $u+iv$ holomorphic.
= Local harmonic conjugate
On a disc, the closed one-form $-u_y\,dx+u_x\,dy$ has a potential $v$ when $\Delta u=0$. The Cauchy--Riemann equations then make $u+iv$ holomorphic.