Regularity of $$\omega $$-minimizers for a class of functionals with non-standard growth

We prove local Hölder continuity results for \(\omega \)-minimizers of a class of functionals with non-standard growth, characterized by the fact of having a double type of degeneracy, and thereby extending to \(\omega \)-minimizers the results obtained in Colombo and Mingione (Arch Ration Mech Anal 215(2):443–496, 2015) for ordinary minimizers. As a side benefit of the proof, we also consider a class of functionals with Orlicz-growth and prove regularity for \(\omega \)-minimizers.