Calculus of Variations and Geometric Measure Theory

P. Baroni

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.


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