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.

引用

页码：1850 / 1864

页数：15

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