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

In this work we prove that the non-negative functions u Lˢ₋₎₂ (), for some s>0, belonging to the De Giorgi classes equationeq0. 1 ₁_ₑ (₁-) (x₀) | (u-k) -|^p\, dx c^{q} \, (x₀, r, k) (kr) ^p (|Bₑ (ₗ_₀) \{u k\|}|Bₑ (x₀) |) ^1-, equation under proper assumptions on, satisfy a weak Harnack inequality with a constant depending on the Lˢ-norm of u. Under suitable assumptions on, the minimizers of elliptic functionals with generalized Orlicz growth belong to De Giorgi classes satisfying eq0. 1; thus this study gives a wider interpretation of Harnack-type estimates derived to double-phase, degenerate double-phase functionals and functionals with variable exponents.