We prove a local higher integrability result for the gradient of solutions to singular, parabolic equations of $p$-Laplacian type. To this end, we show that solutions satisfy a reverse H\"older inequality on intrinsic cylinders, whose geometry depends on the $L^r$-norm of the solution. The exponent $r \geq 2$ allows us to derive estimates in the subcritical range $1 < p \leq 2N/(N+2)$.
"Reverse Hölder inequalities and higher integrability for subcritical parabolic equations." Adv. Differential Equations 17 (1/2) 151 - 172, January/February 2012.