Find the Green function of the first quadrant $x_1>0, x_2>0$.
HINT: Use the Green function of the half space $\Omega:=\left\{x\in\mathbb{R}^n : x_n > 0\right\}$ which is given by\begin{align*} G_n(x,y)&:=E_n(x_1-y_1,\cdots,x_{n-1}-y_{n-1},x_n-y_n)\\ &\quad\ -E_n(x_1-y_1,\cdots,x_{n-1}-y_{n-1},x_n+y_n). \end{align*}
How I can find the Green function of the first quadrant? The difference to the half space is that I have another boundary…