Regularity estimates for the parabolic p(x, t)-Laplacian equation in Besov spaces. (December 2022)

• Record Type: Journal Article
• Authors: Yao, Fengping
• Is Part Of: Nonlinear analysis. Volume 68(2022)
• Publication Date: 2022-12
• Subjects: Besov -- Regularity -- Parabolic -- p(x, t)-Laplacian -- Weak solutions -- Divergence; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103645
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The aim of this paper is to develop the local regularity estimates in Besov spaces for weak solutions to the following parabolic p ( x, t ) -Laplacian equation in divergence form u t − div | ∇ u | p ( x, t ) − 2 a ( x, t ) ∇ u = div F under some proper assumptions on the functions p ( x, t ), a ( x, t ) and F ( x, t ) . Moreover, we want to point out that our results improve the existed results for this kind of problems.