Nonnegative solutions of some quasilinear elliptic inequalities and applications

Details Nonnegative solutions of some quasilinear elliptic inequalities and applications Nonnegative solutions of some quasilinear elliptic inequalities and applications

2010-05-25

arxiv.org/abs/1005.4689v1

Mat. Sb., 2010, Vol. 201, issue 6, http://mi.mathnet.ru/eng/msb7585

Mathematics

Analysis of PDEs

20 pages

Scientific paper

Let $f :\R\to\R$ be a continuous function. We prove that under some
additional assumptions on $f$ and $A:\R\to\R_{+}$, weak $\Cuno$ solutions of
the differential inequality $-\diver(A(\abs{\nabla u})\nabla u)\ge f(u)$ on
$\RN$ are nonnegative. Some extensions of the result in the framework of
subelliptic operators on Carnot Groups are considered.

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