Calculus of Variations and Geometric Measure Theory

A. Nastasi - C. Pacchiano Camacho

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

created by nastasi on 19 Sep 2023


Published Paper

Inserted: 19 sep 2023
Last Updated: 19 sep 2023

Journal: Journal of Differential Equations
Volume: 342
Pages: 121-149
Year: 2022

ArXiv: 2203.07699 PDF


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.