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.
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页码：184 / 194
页数：11
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