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

## TL;DR

This paper proves local H"older continuity of quasiminimizers for a broad class of functionals with Musielak--Orlicz growth, extending previous results with fewer assumptions and establishing key inequalities.

## Contribution

It extends regularity results to more general functionals with non-standard growth and introduces new techniques for establishing H"older continuity.

## Key findings

- Proved local H"older continuity of quasiminimizers.
- Established Harnack's inequality for these minimizers.
- Derived Morrey type estimates for quasiminimizers.

## 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.