Gradient higher integrability for double phase problems on metric measure spaces

Abstract: We study local and global higher integrability properties for quasiminimizers of a class of double-phase integrals characterized by nonstandard growth conditions. We work purely on a variational level in the setting of a metric measure space with a doubling measure and a Poincar\'e inequality. The main novelty is an intrinsic approach to double-phase Sobolev-Poincar\'e inequalities.