Advances in Differential Equations

Reverse Hölder inequalities and higher integrability for subcritical parabolic equations

Andrea Fugazzola

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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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703100

Mathematical Reviews number (MathSciNet)
MR2906732

Subjects
Primary: 35K67: Singular parabolic equations 35K59: Quasilinear parabolic equations 35B65: Smoothness and regularity of solutions

Citation

Fugazzola, Andrea. Reverse Hölder inequalities and higher integrability for subcritical parabolic equations. Adv. Differential Equations 17 (2012), no. 1/2, 151--172. https://projecteuclid.org/euclid.ade/1355703100.


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