Publication at Faculty of Mathematics and Physics |
2019
Abstract
We show that the gradient of the m-power of a solution to a singular parabolic equation of porous medium-type (also known as fast diffusion equation), satisfies a reverse Holder inequality in suitable intrinsic cylinders. Relying on an intrinsic Calderon-Zygmund covering argument, we are able to prove the local higher integrability of such a gradient for m is an element of ((n-2)(+)/n+2, 1).
Our estimates are satisfied for a general class of growth assumptions on the non linearity. In this way, we extend the theory for m >= 1 (see [16] in the list of references) to the singular case.
In particular, an intrinsic metric that depends on the solution itself is introduced for the singular regime. (C) 2019 Elsevier Inc. All rights reserved.