Higher integrability and stability of (p,q)-quasiminimizers

Abstract

Using purely variational methods, we prove local and global higher integrability results for upper gradients of quasiminimizers of a (p,q)-Dirichlet integral with fixed boundary data, assuming it belongs to a slightly better Newtonian space. We also obtain a stability property with respect to the varying exponents p and q. The setting is a doubling metric measure space supporting a Poincaré inequality.