Regularity of K-Quasiminimizers Under Lp&qlogL Double Phase Growth

We study the local quasiminimizers of an integral functional exhibiting Lp&qlogL double phase growth. More precisely, some properties of a special double phase type function in the context of Musielak–Orlicz–Sobolev spaces are obtained. We first get Caccioppoli type and Sobolev–Poincaré type inequalities, then we establish that the gradient of a local quasiminimizer has local higher integrability on a bounded domain. We also get boundary higher integrability on a ball for local quasiminimizers. Finally, we explore the existence of weak solutions to certain double phase Dirichlet problems.