Optimal conditions for a priori estimates for semilinear elliptic systems with two components

被引：5
|
作者：
Li Yuxiang [1 ,2 ]
机构：
[1] Southeast Univ, Dept Math, Nanjing 210096, Peoples R China
[2] Univ Paris 13, Lab Anal Geometrie & Applicat, Inst Galilee, F-93430 Villetaneuse, France
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 3-4期
基金：
中国国家自然科学基金;
关键词：
Elliptic systems; Optimality; L-infinity-regularity; A priori estimates; Existence; POSITIVE SOLUTIONS; SCHRODINGER OPERATOR; WEAK SOLUTIONS; GREEN-FUNCTION; BLOW-UP; EXISTENCE; EQUATIONS; BOUNDS; SINGULARITIES; NONEXISTENCE;
D O I：
10.1016/j.na.2009.09.026
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present a new bootstrap procedure for elliptic systems with two unknown functions. When combined with the L-p-L-q-estimates, it yields the optimal L-infinity-regularity conditions for the three well-known types of weak solutions: H-0(1)-solutions, L-1-solutions and L-delta(1)-solutions. Thanks to the linear theory in L-delta(p)(Omega), it also yields the optimal conditions for a priori estimates for L-delta(1)-solutions. Based on the a priori estimates, we improve known existence theorems for some classes of elliptic systems. (C) 2009 Elsevier Ltd. All rights reserved.
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页码：1850 / 1864
页数：15
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