GLOBAL INTEGRABILITY AND WEAK HARNACK ESTIMATES FOR ELLIPTIC PDES IN DIVERGENCE FORM

被引：7

作者：

Sirakov, Boyan ^{[1
]}

机构：

[1] Pontiffcia Univ Catolica Rio de Janeiro, Dept Matemat, Rio De Janeiro, Brazil

来源：

ANALYSIS & PDE | 2022年 / 15卷 / 01期

关键词：

weak Harnack; Hopf lemma; global integrability; boundary estimates; elliptic PDE; divergence form; FULLY NONLINEAR EQUATIONS; A-PRIORI BOUNDS; SUPERHARMONIC FUNCTIONS; VISCOSITY SOLUTIONS; GROWTH;

D O I：

10.2140/apde.2022.15.197

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that two classically known properties of positive supersolutions of uniformly elliptic PDEs, the boundary point principle (Hopf lemma) and global integrability, can be quantified with respect to each other. We obtain an extension up to the boundary of the De Giorgi-Moser weak Harnack inequality, optimal with respect to the norms involved, for equations in divergence form.

引用

页码：197 / 216

页数：21

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