Inequality of a p-laplacian

Question

Let $\Omega$ be a bounded domain with lipschitzian boundary.$2\leq p$ Why do we have $$\int_{\Omega}\langle|\nabla u|^{p-2}\nabla u- |\nabla v |^{p-2}\nabla v,\nabla v\rangle\leq \int_{\Omega}(|\nabla u|^{p-2}+ |\nabla v |^{p-2})|\nabla u-\nabla v||\nabla v|$$ for all $u,v\in W^{1,p}(\Omega)$?