P-laplacian equation

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

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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