Comparison principles for infinity-Laplace equations in Finsler metrics. (January 2020)

• Record Type: Journal Article
• Authors: Mebrate, Benyam; Mohammed, Ahmed
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: 35B51 -- 35J70 -- 35J75; Comparison principles -- Comparison with quadratic Finsler cones -- Finsler–Minkowski norms -- Normalized Finsler infinity-Laplacian; 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.2019.111605
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study comparison principles for normalized Finsler infinity-Laplace operators with nonhomogeneous terms that depend on solutions and their gradients. This is achieved by using a combination of sup-convolution methods to approximate viscosity solutions by semiconvex functions and finite difference approximation schemes. Characterizations of viscosity subsolutions and supersolutions of equations with constant nonhomogeneous terms through comparison with quadratic Finsler cone are also discussed.