Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Liouville results and asymptotics of solutions of a quasilinear elliptic
  equation with supercritical source gradient term   We consider the elliptic quasilinear equation --$\Delta$ m u = u p
|$\nabla$u| q in R N with q $\ge$ m and p > 0, 1 < m < N. Our main result is a
Liouville-type property, namely, all the positive C 1 solutions in R N are
constant. We also give their asymptotic behaviour : all the solutions in an
exterior domain R N \B r0 are bounded. The solutions in B r0 \ {0} can be
extended as a continuous functions in B r0. The solutions in R N \ {0} has a
finite limit l $\ge$ 0 as |x| $\rightarrow$ $\infty$. Our main argument is a
Bernstein estimate of the gradient of a power of the solution, combined with a
precise Osserman's type estimate for the equation satisfied by the gradient.

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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: stat