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

Bernd Kawohl, Vasilii Kurta
2011 Communications on Pure and Applied Analysis  
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 ≥ v in R n . For the particular case that v ≡ 0 we recover some known Liouville type results. Model cases for the equations involve the p-Laplacian operator for p ∈ [1, 2] and the mean curvature operator.
doi:10.3934/cpaa.2011.10.1747 fatcat:kdkxqcln75ewvdv3jtdu2nijb4