# elliptic equation

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 math.stackexchange.com –  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