Calculus of Variations and Geometric Measure Theory
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L. D'Ambrosio - A. Farina - E. Mitidieri - J. Serrin

Comparison principles, uniqueness and symmetry results of solutions of quasilinear elliptic equations and inequalities

created by farina on 10 Jul 2013


Published Paper

Inserted: 10 jul 2013
Last Updated: 10 jul 2013

Journal: Nonlinear Analysis
Volume: 90
Pages: 135-158
Year: 2013


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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