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

共 50 条

[1] Optimal conditions for L∞-regularity and a priori estimates for semilinear elliptic systems
Li Yuxiang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 351 (01) : 257 - 276
[2] REGULARITY AND A PRIORI ESTIMATES OF SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS
Kosirova, I.
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2010, 79 (02): : 231 - 244
[3] A priori estimates for positive solutions for a class of semilinear elliptic systems
Yarur, CS
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1999, 36 (01) : 71 - 90
[4] EXISTENCE AND A PRIORI ESTIMATES FOR SEMILINEAR ELLIPTIC SYSTEMS OF HARDY TYPE
Pacuta, J.
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2014, 83 (02): : 321 - 330
[5] A-PRIORI ESTIMATES FOR A SEMILINEAR ELLIPTIC PDE
IAIA, JA
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 24 (07) : 1039 - 1048
[6] A priori estimates and existence for strongly coupled semilinear cooperative elliptic systems
Zou, HH
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2006, 31 (05) : 735 - 773
[7] A priori estimates, existence and Liouville theorems for semilinear elliptic systems with power nonlinearities
Quittner, Pavol
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 102 : 144 - 158
[8] A PRIORI ESTIMATES FOR SEMISTABLE SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS
Cabre, Xavier
Sanchon, Manel
Spruck, Joel
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (02) : 601 - 609
[9] Proportionality of Components, Liouville Theorems and a Priori Estimates for Noncooperative Elliptic Systems
Alexandre Montaru
Boyan Sirakov
Philippe Souplet
Archive for Rational Mechanics and Analysis, 2014, 213 : 129 - 169
[10] Proportionality of Components, Liouville Theorems and a Priori Estimates for Noncooperative Elliptic Systems
Montaru, Alexandre
Sirakov, Boyan
Souplet, Philippe
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2014, 213 (01) : 129 - 169

← 1 2 3 4 5 →