Gradient Hölder regularity for degenerate parabolic systems. (December 2022)

• Record Type: Journal Article
• Authors: Bögelein, Verena; Duzaar, Frank; Liao, Naian; Scheven, Christoph
• Is Part Of: Nonlinear analysis. Volume 225(2022)
• Publication Date: 2022-12
• Subjects: 35B65 -- 35K65 -- 35K40 -- 35K55; Degenerate/singular parabolic systems, Hölder continuity of the gradient; 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.2022.113119
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We establish the local Hölder regularity of the spatial gradient of weak solutions to a class of general, degenerate parabolic systems. Our results can be regarded as a generalization of the fundamental work by DiBenedetto and Friedman (1985).