Weighted Lorentz estimate for asymptotically regular parabolic equations of p(x, t)-Laplacian type. (March 2019)

• Record Type: Journal Article
• Authors: Zhang, Junjie; Cai, Maomao; Zheng, Shenzhou
• Is Part Of: Nonlinear analysis. Volume 180(2019)
• Page Start: 225
• Page End: 235
• Publication Date: 2019-03
• Subjects: 35D30 -- 35K55; Parabolic equations of p(x, t)-Laplacian type -- Asymptotically regular -- Weighted Lorentz spaces -- (δ, R)-vanishing condition -- Reifenberg flat domain; 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.2018.10.013
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove a global weighted Lorentz estimate of the spatial gradients of weak solution to the Cauchy–Dirichlet problem for asymptotically regular parabolic equations of p ( x, t ) -Laplacian type in a Reifenberg flat domain. It is mainly assumed that the associated regular nonlinearity is measurable with respect to the time variable and satisfies the ( δ, R ) -vanishing condition with respect to the spatial variables.