Gradient higher integrability for singular parabolic double-phase systems

Abstract

AbstractWe prove a local higher integrability result for the gradient of a weak solution to parabolic double-phase systems of p-Laplace type when $$\tfrac{2n}{n+2}< p\le 2$$ 2 n n + 2 < p ≤ 2 . 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.