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Questions involving the $p$-Laplace operator $\Delta_p u=\operatorname{div}(|\nabla u|^{p-2}\nabla u)$.

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Trick in a inequality of a paper of free boundary problem that involves the p-laplacian with...

This is really a comment on the response posted above: for $\xi,\eta\neq 0$, using $|\xi|\leq (|\xi|^2+|\eta|^2)^{1/2}$ and $|\eta|\leq (|\xi|^2+|\eta|^2)^{1/2}$ one obtains $$|\xi|+|\eta|\leq 2(|\xi| …
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