Published Paper

Inserted: 19 sep 2023
Last Updated: 19 sep 2023

Journal: Journal of Differential Equations
Volume: 342
Pages: 121-149
Year: 2022
Doi: https://doi.org/10.1016/j.jde.2022.09.031

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 Poincar\'e inequality.