# Does the function need to be convex in order to satisfy the following functional?

If $\Omega \subset R^n$ and function $f(x,p)$ is strictly convex in $p$ . Is the solution to the functional $$F(u)= \int_{\Omega}f(x,Du(x))dx$$

unique in some class $C$ , and why should it be convex ?

I tried finding the hessian of the function, but that doesn't seem to help ? I need some tips. Thanks

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 What is the $\Omega$ used for? – Henning Makholm Nov 14 '12 at 20:58 @HenningMakholm : Sir , i have edited . – Theorem Nov 14 '12 at 21:03 I don't know what it means for a function to satisfy a functional. – user53153 Dec 20 '12 at 2:54