Slope estimate and boundary differentiability of infinity harmonic functions on convex domains. (July 2016)

• Record Type: Journal Article
• Authors: Hong, Guanghao; Liu, Dawei
• Is Part Of: Nonlinear analysis. Volume 139(2016)
• Page Start: 158
• Page End: 168
• Publication Date: 2016-07
• Subjects: 49N60 -- 35J67; Infinity harmonic function -- Boundary differentiability -- Convex domain -- Slope function; 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.2016.02.018
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the boundary differentiability of infinity harmonic functions with given differentiable boundary data on convex domains. At a flat point (the boundary point where the blow-up of the domain is the half-space), the infinity harmonic function u is differentiable due to a previous result of the first author in Hong (2013). At a corner point (the boundary point where the blow-up of the domain is not the half-space), an example shows that u is not necessarily differentiable. In this paper, we establish a slope estimate for u at corner points and provide a necessary and sufficient condition for the differentiability of u at corner points.