Twice differentiability of solutions to fully nonlinear parabolic equations near the boundary. (August 2020)

• Record Type: Journal Article
• Authors: Adimurthi, Karthik; Banerjee, Agnid; Verma, Ram Baran
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: primary 35J60 -- secondary 35D40; 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.2020.111830
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we prove H 2 + α regularity for viscosity solutions to non-convex fully nonlinear parabolic equations near the boundary. This constitutes the parabolic counterpart of a similar C 2, α regularity result due to Silvestre and Sirakov proved in [17] for solutions to non-convex fully nonlinear elliptic equations.