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

@article{Harjulehto2019HlderCO,
title={H{\"o}lder continuity of \$\omega\$-minimizers of functionals with generalized Orlicz growth},
author={Petteri Harjulehto and Peter A. Hasto and Mikyoung Lee},
journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE},
year={2019}
}
• Published 5 June 2019
• Mathematics
• ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
We show local Holder 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 Holder continuity for $\omega$-minimizers.
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