Optimal conditions for L∞-regularity and a priori estimates for semilinear elliptic systems

被引：4

作者：

Li Yuxiang ^{[1
,2
]}

机构：

[1] Southeast Univ, Dept Math, Nanjing 210096, Peoples R China

[2] Univ Paris 13, Inst Galilee, Lab Anal Geometrie & Applicat, F-93430 Villetaneuse, France

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 351卷 / 01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; REACTION-DIFFUSION SYSTEM; POSITIVE SOLUTIONS; BLOW-UP; VARIATIONAL STRUCTURE; SCHRODINGER OPERATOR; WEAK SOLUTIONS; EXISTENCE; EQUATIONS; NONEXISTENCE; BOUNDS;

D O I：

10.1016/j.jmaa.2008.10.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a bootstrap procedure for semilinear elliptic systems with n (>= 3) components. Combining with the L-p-L-q-estimates, if yields the optimal L-infinity-regularity conditions for the three well known types of weak Solutions: H-0(1)-soultions, 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) 2008 Elsevier Inc. All rights reserved.

引用

页码：257 / 276

页数：20

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