Gradient higher integrability of bounded solutions to parabolic double-phase systems

Abstract

We prove that bounded solutions to degenerate parabolic double-phase problem modelled upon \[u_t-\dv(|\na u|^{p-2}\na u+a(x,t)|\na u|^{q-2}\na u)=-\dv(|F|^{p-2}F+a(x,t)|F|^{q-2}F)\,, \] where a nonnegative weight $a$ is $\hat{I}\pm$-Hölder continuous in space and $\frac{\hat{I}}{\pm }2$-Hölder continuous in time, have locally higher integrable gradients for the sharp range of exponents $p<q\le p+\hat{I}\pm$.