Maximum principles, Liouville theorem and symmetry results for the fractional g-Laplacian

Abstract

We study different maximum principles for non-local non-linear operators with non-standard growth that arise naturally in the context of fractional Orlicz–Sobolev spaces and whose most notable representative is the fractional g-Laplacian: [Formula presented] being g the derivative of a Young function. We further derive qualitative properties of solutions such as a Liouville type theorem and symmetry results and present several possible extensions and some interesting open questions. These are the first results of this type proved in this setting.