I got the following nonlinear functional $$J\left(u\right)=\frac{1}{2}\int_{\Omega}\left[H\left(\nabla u\right)\right]^2\;dx-\int_{\Omega}f\cdot u\;dx,\;\forall\;v\in X$$, where $H$ is a Finsler norm, who is convex.
How to prove that this functional is strongly convex?