The weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth

In this work we prove that the non-negative functions belonging to suitable non-homogeneous (non-uniformly elliptic) De Giorgi classes, satisfy a weak Harnack inequality with a constant depending on the Ls-norm of the solution. Under suitable assumptions, the minimizers of elliptic functionals with generalized Orlicz growth belong to De Giorgi classes satisfying the above condition; thus this study gives a wider interpretation of Harnack-type estimates derived to double-phase, degenerate double-phase functionals and functionals with variable exponents.