Gehring's lemma for metrics and higher integrability of the gradient for minimizers of noncoercive variational functionals
Volume 120 / 1996
Studia Mathematica 120 (1996), 1-22 DOI: 10.4064/sm-120-1-1-22
We prove a higher integrability result - similar to Gehring's lemma - for the metric space associated with a family of Lipschitz continuous vector fields by means of sub-unit curves. Applications are given to show the higher integrability of the gradient of minimizers of some noncoercive variational functionals.