Regularity results for generalized double phase functionals

Abstract

We consider a wide class of functionals with the property of changing their growth and ellipticity properties according to the modulating coefficients in the framework of Musielak–Orlicz spaces. In particular, we provide an optimal condition on the modulating coefficient to establish the Hölder regularity and Harnack inequality for quasiminimizers of the generalized double phase functional with $\left(G,H\right)$-growth for two Young functions $G$ and $H$.