Singular parabolic equations, measures satisfying density conditions, and gradient integrability. (April 2017)

• Record Type: Journal Article
• Authors: Baroni, Paolo
• Is Part Of: Nonlinear analysis. Volume 153(2017)
• Page Start: 89
• Page End: 116
• Publication Date: 2017-04
• Subjects: 35R06 -- 35K65 -- 35B65; Measure data problems -- Singular parabolic equations -- Marcinkiewicz spaces; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.10.019
• Languages: English
• ISSNs: 0362-546X

Abstract

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.