A note on the weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth

Abstract

We prove the weak Harnack inequality for the functions $u$ which belong to the corresponding De Giorgi classes $D{G}^{-}(\Omega )$ under the additional assumption that $u\in L_{loc}^s(\Omega )$ with some $s>0$. In particular, our result covers new cases of functionals with a variable exponent or double-phase functionals under the non-logarithmic condition.