Quantitative Local Bounds for Subcritical Semilinear Elliptic Equations

被引：9

作者：

Bonforte, Matteo ^{[1
]}

Grillo, Gabriele ^{[2
]}

Luis Vazquez, Juan ^{[1
]}

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[2] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

MILAN JOURNAL OF MATHEMATICS | 2012年 / 80卷 / 01期

关键词：

Local bounds; semilinear elliptic equations; regularity; Harnack inequality; POSITIVE SOLUTIONS; WEAK SOLUTIONS; DELTA-U; SUPERLINEAR PROBLEMS; EXISTENCE; DOMAINS; REGULARITY; BEHAVIOR; INEQUALITIES; CONVERGENCE;

D O I：

10.1007/s00032-012-0183-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to prove local upper and lower bounds for weak solutions of semilinear elliptic equations of the form -Delta u = cu (p) , with 0 < p < p (s) = (d + 2)/(d - 2), defined on bounded domains of , without reference to the boundary behaviour. We give an explicit expression for all the involved constants. As a consequence, we obtain local Harnack inequalities with explicit constants, as well as gradient bounds.

引用

页码：65 / 118

页数：54

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