Self-improving property of degenerate parabolic equations of porous medium-type

Abstract

We show that the gradient of solutions to degenerate parabolic equations of porous medium-type satisfies a reverse Hölder inequality in suitable intrinsic cylinders. We modify the by-now classical Gehring lemma by introducing an intrinsic Calderón-Zygmund covering argument, and we are able to prove local higher integrability of the gradient of a proper power of the solution $u$.

With respect to the previous version, a detailed application of a proper Vitali covering is given here

References in corpus (2)

• Riesz potentials and nonlinear parabolic equations
• Pointwise Calderón-Zygmund gradient estimates for the $p$-Laplace system

Cited by in corpus (8)

• Higher integrability for doubly nonlinear parabolic systems
• Self-improving property of the fast diffusion equation
• Optimal regularity in time and space for the porous medium equation
• A reverse Hölder inequality for the gradient of solutions to Trudinger's equation
• Higher integrability for parabolic systems with Orlicz growth
• Higher integrability for the singular porous medium system
• Higher integrability and stability of $(p,q)$-quasiminimizers
• Higher integrability in the obstacle problem for the fast diffusion equation