Gradient higher integrability for singular parabolic double-phase systems

Abstract

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}$$\ frac{2n}{n+2}< p\\le 2$$\\end{document}. The result is based on a reverse Hölder inequality in intrinsic cylinders combining p-intrinsic and (p, q)-intrinsic geometries. A singular scaling deficits affects the range of q.