Higher integrability of minimizing Young measures

We prove local higher integrability with large exponents for minimizers and Young measure minimizers of variational integrals of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \int_{\Omega} \! F(x,\nabla u(x)) dx $$\end{document} where F is a Carathéodory integrand that resembles the p-Dirichlet integrand at infinity. The result yields existence of minimizing sequences with higher equi-integrability properties locally in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Omega$\end{document}.