2026-04-02 15:51:58.1775145118
the question I'm struggling a bit with is:
let h be a harmonic function in a simply connected space $D$, prove that there exists an analytic $f=u+iv$ in $D$ s.t $u+v=h$
I tried to solve by placing $h= u+iv$ into the equation given by h's harmonic attributes:
$\Delta h = h_{xx} + h_{yy} = 0$
but couldn't continue to the proof without assuming f is analytic which kind of defeats the purpose if I understood the question correctly. Can I get a hint/tips ?
let h be a harmonic function in a simply connected space $D$, prove that there exists an analytic $f=u+iv$ in $D$ s.t $u+v=h$
66 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail Atthe question I'm struggling a bit with is:
let h be a harmonic function in a simply connected space $D$, prove that there exists an analytic $f=u+iv$ in $D$ s.t $u+v=h$
I tried to solve by placing $h= u+iv$ into the equation given by h's harmonic attributes:
$\Delta h = h_{xx} + h_{yy} = 0$
but couldn't continue to the proof without assuming f is analytic which kind of defeats the purpose if I understood the question correctly. Can I get a hint/tips ?
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