Stability of quasiminimizers of the p -Dirichlet integral with varying p on metric spaces

Abstract

We prove a stability result, with respect to the varying exponent p, for a family of quasiminimizers of the p-Dirichlet energy functional on a doubling metric measure space. In addition, we prove global higher integrability for upper gradients of quasiminimizers with fixed boundary data, provided that the boundary data belong to a slightly better Newtonian space.