Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Hi guys, in what sense the p-Laplacian is degenerate for p greater than 2 and singular for p smaller than 2 ? Thank you!

share|improve this question
I assume you should just look at the "directional derivative" $\frac{d}{dt} \Delta_p (f+tg)$. At the points where $\nabla f =0$, the expression you get is singular for $p<2$ and vanishes for $p>2$ (degenerate pointing at a vanishing of the derivative). –  Antoine Mar 13 '13 at 12:09
For a longer answer see math.stackexchange: math.stackexchange.com/questions/306320/… –  Tommi Brander Apr 10 '13 at 15:37

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.