1
Trouver les applications \(G: \Rr^2 \to \Rr\) de classe \(C^2\) telles que \(\frac{\partial ^2 G}{\partial x \partial y}=0\).
2
Trouver les applications \(F:\Rr^2 \to \Rr\) de classe \(C^2\) solutions de \[\frac{\partial ^2 F}{\partial x^2} - \frac{\partial ^2 F}{\partial y^2}=0 \;\; .\] (Indication: poser \(\varphi (u,v) = \frac{1}{2}(u+v,u-v)\) et \(G=F\circ \varphi\) ).