Maximum principle for Pucci equations with sublinear growth in Du and its applications. (September 2017)

• Record Type: Journal Article
• Authors: Koike, Shigeaki; Kosugi, Takahiro
• Is Part Of: Nonlinear analysis. Volume 160(2017)
• Page Start: 1
• Page End: 15
• Publication Date: 2017-09
• Subjects: ABP maximum principle -- Weak Harnack inequality -- p-Laplace operator; 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.2017.03.018
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: It is obtained that there exist strong solutions of Pucci extremal equations with sublinear growth in D u and measurable ingredients. It is proved that a strong maximum principle holds in a local sense in Lemma 4.1 although even the (weak) maximum principle fails. By using this existence result, it is shown that the ABP type maximum principle and the weak Harnack inequality for viscosity solutions hold true. As an application, the Hölder continuity for viscosity solutions of possibly singular, quasilinear equations is established.