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How to prove that (2) is the fundamental solution (1)???

$\frac{\partial}{\partial x}\left(P\frac{\partial\varphi}{\partial x}\right)+\frac{\partial}{\partial y}\left(P\frac{\partial\varphi}{\partial y}\right)=0$ (1)

$\Phi=-\varphi_0\ln r+f$ (2)

$\varphi_0$ - solution of (1) ($\varphi_0(M,N)=1$ if $M=N$)

$f$ - belongs $C^{(2)}$ ($f(M,N)=0$ if $M=N$)

$r=\sqrt{(x-\xi)^2+(y-\eta)^2}$, $M(x,y)$, $N(\xi,\eta)$

(1) - Elliptic Equations

P.S. always possible to allocate the logarithm of the fundamental solutions of elliptic type?

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What is $P$ here? –  Ben McKay May 6 '13 at 20:56
$P=P(M)$, $M(x,y)$. as minimum $P\in C^(1)$. –  eiler13 May 6 '13 at 21:45
sorry $C^{(1)}$ –  eiler13 May 6 '13 at 21:47
And what is $M$ and $N$? This question is not very clearly written in the state it is. But I suspect that it may be outside the scope of this website. (Please see the FAQ for what kinds of questions are generally asked here.) You may have better luck with –  Willie Wong May 7 '13 at 7:26
$M(x,y)$ - observation point $N(\xi,\eta)$ - the location of drain (singular point) –  eiler13 May 7 '13 at 8:22

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