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Using a variant of Caccioppoli's inequality involving small weights, i.e.weights of the form $(1+|\nabla u|^2)^{-\alpha/2}$ for some $\alpha > 0$, weestablish several Liouville-type theorems under general non-standard growthconditions.

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