Let there be a Green function $G(x,y,x_0,y_0)$ for $D={(x,y)\in{\Re}^2|x^2+2y^2<7}$ and let $(x_0,y_0)$ be any point within $D$. Calculate the integral:
$$u(x,y) = \oint_{\partial D} G_{\vec{n}}(x,y,x_0,y_0)ds$$
So neither of the paths I can clearly see how to do. First path when I see $f=1$ and try to guess $u$ via.
$$\Delta u = 0 $$
$$u|_{\partial D}=f=1$$
Or try the other path to get $u$ via setting the Green function and then integrating.
Any help would be welcome.