On a Liouville-type comparison principle for solutions of quasilinear elliptic inequalities

Abstract

We characterize in terms of monotonicity basic properties of quasilinear elliptic partial differential operators which make it possible to obtain a Liouville-type comparison principle for entire solutions of quasilinear elliptic partial differential inequalities of the form A( u)+| u| q−1 u⩽ A( v)+| v| q−1 v, which belong only locally to the corresponding Sobolev spaces on R n, n⩾2 . We establish that such properties are inherent for a wide class of quasilinear elliptic partial differential operators. Typical examples of such operators are the p-Laplacian and its well-known modifications for 1< p⩽2. To cite this article: V.V. Kurta, C. R. Acad. Sci. Paris, Ser. I 336 (2003).