Published Paper
Inserted: 10 jul 2013
Last Updated: 10 jul 2013
Journal: Nonlinear Analysis
Volume: 90
Pages: 135-158
Year: 2013
Abstract:
We prove comparison principles, uniqueness, regularity and symmetry results for $p$-regular distributional solutions of quasilinear very weak elliptic equations of coercive type and to related inequalities. The simplest model examples are
$-\Delta_p u+ \vert u \vert^{q-1} u =h \quad on \quad R^N$,
where $q>p-1>0$ and
$ -div \left(\frac{\nabla u}{\sqrt{1+\vert{\nabla u}\vert^2}} \right) + \vert u \vert^{q-1}u =h \quad on\quad R^N,$
with $q>0$ and $h\in L^1_{loc}(R^N) $.
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