H\"older continuity of $\omega$-minimizers of functionals with generalized Orlicz growth

Abstract

We show local H\"older continuity of quasiminimizers of functionals with non-standard (Musielak--Orlicz) growth. Compared with previous results, 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 continuity for $\omega$-minimizers.