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

created by baroni on 27 Oct 2016

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Submitted Paper

Inserted: 27 oct 2016
Last Updated: 27 oct 2016

Year: 2016

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.