Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The known Poincaré inequality says that in the conditions of the theorem we have \begin{equation} \|u - u_{\Omega}\|_{L^{p}(\Omega)} \le C \| \nabla u \|_{L^{p}(\Omega)}. \end{equation} see for instance [1] Can we obatain also \begin{equation} \|u - u_{\Omega}\|_{L^{p}(\Omega)} \le C \| \nabla u - (\nabla u)_{\Omega} \|_{L^{p}(\Omega)}. \end{equation}


share|cite|improve this question
up vote 4 down vote accepted

No; take $u(x) = a\cdot x$ for some constant vector $a$. Then the right side vanishes but the left does not.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.