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

[41] Fractional integration and optimal estimates for elliptic systems
Hernandez, Felipe
Spector, Daniel
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2024, 63 (05)
[42] Sharp a priori estimates for a class of nonlinear elliptic equations with lower order terms
A. Alvino
V. Ferone
A. Mercaldo
Annali di Matematica Pura ed Applicata (1923 -), 2015, 194 : 1169 - 1201
[43] A PRIORI ESTIMATES FOR ELLIPTIC PROBLEMS WITH A STRONGLY SINGULAR GRADIENT TERM AND A GENERAL DATUM
Giachetti, Daniela
Petitta, Francesco
Segura de Leon, Sergio
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2013, 26 (9-10) : 913 - 948
[44] A priori estimates and bifurcation of solutions for an elliptic equation with semidefinite critical growth in the gradient
Souplet, Philippe
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 121 : 412 - 423
[45] A priori estimates for elliptic equations with reaction terms involving the function and its gradient
Bidaut-Veron, Marie-Francoise
Garcia-Huidobro, Marta
Veron, Laurent
MATHEMATISCHE ANNALEN, 2020, 378 (1-2) : 13 - 56
[46] Sharp a priori estimates for a class of nonlinear elliptic equations with lower order terms
Alvino, A.
Ferone, V.
Mercaldo, A.
ANNALI DI MATEMATICA PURA ED APPLICATA, 2015, 194 (04) : 1169 - 1201
[47] A priori estimates for elliptic equations with gradient dependent term and zero order term
Alvino, A.
Betta, M. F.
Mercaldo, A.
Volpicelli, R.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 302 : 550 - 584
[48] Nonexistence of nonnegative entire solutions of semilinear elliptic systems
Gladkov, Alexander
Sergeenko, Sergey
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2022, 67 (01) : 49 - 60
[49] POINTWISE ESTIMATES FOR SYSTEMS OF COUPLED p -LAPLACIAN ELLIPTIC EQUATIONS
Aghajani, Asadollah
Shahgholian, Henrik
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2023, 22 (03) : 899 - 921
[50] OPTIMAL A PRIORI ERROR ESTIMATES FOR AN ELLIPTIC PROBLEM WITH DIRAC RIGHT-HAND SIDE
Koeppl, T.
Wohlmuth, B.
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (04) : 1753 - 1769

← 1 2 3 4 5 →