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If I know that $x\rightarrow G(x,y)$ is harmonic with respect to y, why $\frac{\partial G}{\partial y}(x,y)$ is also harmonic with respect to y? $x,y\in R^n$.

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Why do you write $x \rightarrow G(x,y)?$ –  Will Jagy Nov 2 '12 at 19:28
Hint: Show that every harmonic function is infinitely differentiable. –  Alexander Sibelius Nov 2 '12 at 19:29
Probably, you should be explicit about what $x$ and $y$ are (I suspect they are vectors...) and what excatly do you mean by harmonic: with respect to all variables? Being explicit seldom hurts! –  Mariano Suárez-Alvarez Nov 2 '12 at 19:31
Hi, I think question is more clear now. I can give more details if you want. –  TheStudent Nov 2 '12 at 19:42

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