Gradient higher integrability for singular parabolic double-phase systems

We prove a local higher integrability result for the gradient of a weak solution to parabolic double-phase systems of p-Laplace type when 2nn+2<p <= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tfrac{2n}{n+2}< p\le 2$$\end{document}. The result is based on a reverse Holder inequality in intrinsic cylinders combining p-intrinsic and (p, q)-intrinsic geometries. A singular scaling deficits affects the range of q.