A Liouville comparison principle for solutions of
singular quasilinear elliptic second-order partial differential
Bernd Kawohl - Mathematisches Institut, Universität zu Köln, 50923 Köln, Germany (email)
Abstract: 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.
Keywords: Liouville theorem, comparison principle, quasilinear elliptic equation, singular elliptic equation.
Received: March 2011; Revised: April 2011; Published: May 2011.
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