B. Franchi et Fs. Cassano, GEHRINGS LEMMA FOR METRICS AND HIGHER INTEGRABILITY OF THE GRADIENT FOR MINIMIZERS OF NONCOERCIVE VARIATIONAL FUNCTIONALS, Studia Mathematica, 120(1), 1996, pp. 1-22
We prove a higher integrability result-similar to Gehring's lemma-for
the metric space associated with a family of Lipschitz continuous vect
or fields by means of sub-unit curves. Applications are given to show
the higher integrability of the gradient of minimizers of some noncoer
cive variational functionals.