I need to find the euler lagrange solution, meaning the function $f$ that minimizes:
$$\min_f \int_{}^{} \int_{}^{} \: (\nabla f(x,y) - \nabla s(x,y))^2 \: \: dxdy $$
When we fully know $s(x,y)$, and we know $f(x,y)$ on the boundaries of the integral.