Reverse Hölder inequalities and higher integrability for subcritical parabolic equations (Q664633)

The author considers singular parabolic equations of \(p\)-Laplacian type. \textit{J. Kinnunen} and \textit{J. L. Lewis} [Duke Math. J. 102, No. 2, 253--271 (2000; Zbl 0994.35036)] proved that a higher integrability result holds if \(p > \frac{2N}{N+2}\) where \(N\) is the dimension of the space. In this paper the author proves the higher integrability property assuming an extra assumption on the solution: i.e. the solution belongs locally to a suitable \(L^r\) where \(r\) is a positive number such that the quantity \(N(p-2) + rp\) is positive. The author uses an approach based on Gehring covering lemma and on the intrinsic geometry introduced by DiBenedetto.