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\\