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A Liouville comparison principle for solutions of singular quasilinear elliptic second-order partial differential inequalities

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  • We compare entire weak solutions $u$ and $v$ of quasilinear partial differential inequalities on $R^n$ without any assumptions on their behaviour at infinity and show among other things, that they must coincide if they are ordered, i.e. if they satisfy $u\geq v$ in $R^n$. For the particular case that $v\equiv 0$ we recover some known Liouville type results. Model cases for the equations involve the $p$-Laplacian operator for $p\in[1,2]$ and the mean curvature operator.
    Mathematics Subject Classification: Primary: 35B53 35J62; Secondary: 35B51, 35J75, 35J92, 35J93.


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