Generalized superharmonic functions with strongly nonlinear operator

Abstract

We study properties of $\mathcal{A}$-harmonic and $\mathcal{A}$-superharmonic functions involving an operator having generalized Orlicz-growth embracing besides Orlicz case also natural ranges of variable exponent and double-phase cases. In particular, Harnack's Principle and Minimum Principle are provided for $\mathcal{A}$-superharmonic functions and boundary Harnack inequality is proven for $\mathcal{A}$-harmonic functions.