Small weights in Caccioppoli's inequality and applications to Liouville-type theorems for non-standard problems

Abstract

Using a variant of Caccioppoli's inequality involving small weights, i.e. weights of the form (1 + |∇u| 2 ) −α/2 for some α > 0, we establish several Liouville-type theorems under general non-standard growth conditions. 1 Dedicated to the 70th birthday of Gregory Seregin