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.
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页码：65 / 118
页数：54
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