Marcinkiewicz regularity for singular parabolic p-Laplace type equations with measure data. (October 2022)

• Record Type: Journal Article
• Authors: Park, Jung-Tae
• Is Part Of: Nonlinear analysis. Volume 223(2022)
• Publication Date: 2022-10
• Subjects: primary 35K92 -- secondary 35R06 35B65; Singular parabolic equation -- Measure data -- Marcinkiewicz space; 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.2022.113073
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider quasilinear parabolic equations with measurable coefficients when the right-hand side is a signed Radon measure with finite total mass, having p -Laplace type: u t − div a ( D u, x, t ) = μ in Ω × ( 0, T ) ⊂ R n × R . In the singular range 2 n n + 1 < p ≤ 2 − 1 n + 1, we establish regularity estimates for the spatial gradient of solutions in the Marcinkiewicz spaces, under a suitable density condition of the right-hand side measure.