Maximum principle for Pucci equations with sublinear growth in Du and its applications

被引：1

作者：

Koike, Shigeaki ^{[1
]}

Kosugi, Takahiro ^{[1
]}

机构：

[1] Tohoku Univ Aoba, Math Inst, Sendai, Miyagi 9808578, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 160卷

关键词：

ABP maximum principle; Weak Harnack inequality; p-Laplace operator; FULLY NONLINEAR EQUATIONS; UNIFORMLY ELLIPTIC-EQUATIONS; VISCOSITY SOLUTIONS; HARNACK INEQUALITY; WEAK; EQUIVALENCE; INGREDIENTS;

D O I：

10.1016/j.na.2017.03.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is obtained that there exist strong solutions of Pucci extremal equations with sublinear growth in Du 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 Holder continuity for viscosity solutions of possibly singular, quasilinear equations is established. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：1 / 15

页数：15

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