# Existence and nonexistence results for anisotropic quasilinear elliptic equations

created on 29 Jul 2003
modified by gazzola on 19 Jan 2005

[BibTeX]

Published Paper

Inserted: 29 jul 2003
Last Updated: 19 jan 2005

Journal: Ann. Inst. H. Poincaré
Year: 2003

Abstract:

We consider a new class of quasilinear elliptic equations with a power-like reaction term: the differential operator weights partial derivatives with different powers, so that the underlying functional-analytic framework involves anisotropic Sobolev spaces. Critical exponents for embeddings of these spaces into $L^q$ have two distinct expressions according to whether the anisotropy is concentrated'' or spread out''. Existence results in the subcritical case are affected by this dichotomy. On the other hand, nonexistence results are obtained in the at least critical case in domains with a geometric property which modifies the standard notion of starshapedness.