0
$\begingroup$

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 ?

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.