Hölder continuity of $\omega$-minimizers of functionals with generalized Orlicz growth

We show local H older continuity of quasiminimizers of function- als with non-standard (Musielak–Orlicz) growth. Compared with previous re- sults, we cover more general minimizing functionals and need fewer assumptions. We prove Harnack’s inequality and a Morrey type estimate for quasiminimizers. Combining this with Ekeland’s variational principle, we obtain local H older con- tinuity for !-minimizers.