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  • https://math.libretexts.org/Bookshelves/Differential_Equations/Partial_Differential_Equations_(Miersemann)/7%3A_Elliptic_Equations_of_Second_Order/7.4.0%3A_Green's_Function_for_Delta
    A function \(G(y,x)\), \(y,\ x\in\overline{\Omega}\), \(x\not= y\), is called Green function associated to \(\Omega\) and to the Dirichlet problem (7.3.1.1), (7.3.1.2) if for fixed \(x\in\Omega\), tha...A function \(G(y,x)\), \(y,\ x\in\overline{\Omega}\), \(x\not= y\), is called Green function associated to \(\Omega\) and to the Dirichlet problem (7.3.1.1), (7.3.1.2) if for fixed \(x\in\Omega\), that is we consider \(G(y,x)\) as a function of \(y\), the following properties hold: \left(G(y,x^{(1)})\frac{\partial}{\partial n_y}G(y,x^{(2)})-G(y,x^{(2)})\frac{\partial}{\partial n_y}G(y,x^{(1)})\right) dS_y\\

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