Reverse Hölder inequalities and higher integrability for subcritical parabolic equations

Andrea Fugazzola

Abstract

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 $1 < p \leq 2N/(N+2)$.

Article information

Source
Adv. Differential Equations, Volume 17, Number 1/2 (2012), 151-172.

Dates
First available in Project Euclid: 17 December 2012