# Maximal monotone functional

Given a bounded domain $$\Omega$$ $$h:W^{1,p}(\Omega)\rightarrow W^{1,p}(\Omega)^*$$ defined by $$h(u)=\int_{\Omega}|Du|^{p-2}(Du,Dh)_{\mathbb{R}^N}dz$$ why is it continuous and maximal monotone ?

• because it is the subgradient of a convex and continuous function – daw May 22 at 6:34
• How can we show it is continuous – Mono May 22 at 6:44
• Continuity follows from Hölder's inequality. – gerw May 22 at 17:22