Geodesic
Small weights in Caccioppoli's inequality and applications to Liouville-type theorems for non-standard problems
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 49, Tome 508 (2021), pp. 73-88

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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 $\alpha > 0$, we establish several Liouville-type theorems under general non-standard growth conditions. 
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     author = {M. Bildhauer and M. Fuchs},
     title = {Small weights in {Caccioppoli's} inequality and applications to {Liouville-type} theorems for non-standard problems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {73--88},
     publisher = {mathdoc},
     volume = {508},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_508_a2/}
}
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M. Bildhauer; M. Fuchs. Small weights in Caccioppoli's inequality and applications to Liouville-type theorems for non-standard problems. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 49, Tome 508 (2021), pp. 73-88. http://geodesic.mathdoc.fr/item/ZNSL_2021_508_a2/