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

Let $\Omega $ be a domain, $u \in H^{1}(\Omega)$ and $\xi \in C^{\infty}_{0}(\{u > 0\})$ you can assume that $\{u > 0\}$ is an open set. I'd like to know if in this situation we can conclude that $$ 0 = \lim_{\varepsilon \rightarrow o^+} \int_{\Omega} \dfrac{ \chi( u + \varepsilon \xi >0 ) - \chi(\{ u>0 \} ) }{\varepsilon}? $$ Where $\chi(A) $ is the characteristc function of a set $A$. Or if can I assume another similar condition for that the limit above be true. This ask is motivated for instance by the question here. I've also read other things that motivate this suspicion.

share|cite|improve this question
user: There is no need to make your title larger than other titles to questions. It is perfectly legible as is. – amWhy Nov 25 '12 at 2:21

Your Answer


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

Browse other questions tagged or ask your own question.