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Does anyone know where I can find a proof of the existence of Green's function, $G(x,x_0)$ on any nice enough domain $\Omega \subset \mathbb{R}^n$?

Edit: This is for Laplace's problem

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  • $\begingroup$ For which problem? $\endgroup$ – Tryss Apr 11 '15 at 22:53
  • $\begingroup$ Laplace's problem $\endgroup$ – User112358 Apr 11 '15 at 22:56
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    $\begingroup$ I assume this is for the Dirichlet problem for the Laplace equation, though clarification would be nice. If I am correct, any text on classical potential theory, e.g. the text by Armitage and Gardiner, will have a proof. This particular text is probably more general than you want, but it does contain most of a proof for the case of a $C^2$ boundary (some of it is left to exercises). $\endgroup$ – Ian Apr 11 '15 at 22:57

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