# Singular parabolic equations, measures satisfying density conditions, and gradient integrability

created by baroni on 27 Oct 2016
modified on 30 Mar 2018

[BibTeX]

Published Paper

Inserted: 27 oct 2016
Last Updated: 30 mar 2018

Journal: Nonlinear Analysis
Volume: 153
Year: 2017
Doi: 10.1016/j.na.2016.10.019

Abstract:

We consider solutions to singular parabolic equations with measurable dependence on the $(x, t)$ variables and having on the right-hand side a measure satisfying a density condition. We prove that the less the measure is concentrated, the more the gradient is regular, in the Marcinkiewicz scale. We provide local estimates and recover some classic results.