A new method of proving a priori bounds for superlinear elliptic PDE

被引：5

作者：

Sirakov, Boyan ^{[1
]}

机构：

[1] PUC Rio, Dept Matemat, BR-22451900 Gavea, RJ, Brazil

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2020年 / 141卷

关键词：

A priori bounds; Elliptic equations; Superlinear; Positive solutions; FULLY NONLINEAR EQUATIONS; POSITIVE SOLUTIONS; VISCOSITY SOLUTIONS; EXISTENCE; THEOREMS;

D O I：

10.1016/j.matpur.2020.07.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We describe a new method of proving a priori bounds for positive supersolutions and solutions of superlinear elliptic PDE, based on global weak Harnack inequalities and a quantitative Hopf lemma. Novel results based on the method include: (i) equations without a boundary condition on the whole boundary; (ii) equations with nonlinearities which do not have precise growth at infinity; (iii) systems of inequalities with opposite sign. (C) 2020 Elsevier Masson SAS. All rights reserved.

引用

页码：184 / 194

页数：11

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