Green matrices and continuity of the weak solutions for the elliptic systems with lower order terms

被引：2

作者：

Zhuge, Jinping ^{[1
]}

Zhang, Zhenqiu ^{[2
,3
]}

机构：

[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2016年 / 27卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Elliptic systems; Kato-Stummel class; Green matrices; continuity; Holder continuity; Schauder estimate; HARNACK INEQUALITY; EQUATIONS;

D O I：

10.1142/S0129167X16500105

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the second-order elliptic systems with lower order terms coefficients belonging to Kato-Stummel type classes in a bounded domain Omega subset of R-n, where n >= 3. We establish the existence, global pointwise estimates and L-p estimates for Green matrices. Based on these estimates, we are able to show the continuity of weak solutions for the general elliptic systems by using method of potentials. We also obtain the optimal Schauder estimates for weak solutions.

引用

页数：34

共 50 条

[21] Behavior of solutions of quasilinear elliptic inequalities containing terms with lower-order derivatives
A. A. Kon'kov
Mathematical Notes, 1998, 64 : 817 - 821
[22] Behavior of solutions of quasilinear elliptic inequalities containing terms with lower-order derivatives
Kon'kov, AA
MATHEMATICAL NOTES, 1998, 64 (5-6) : 817 - 821
[23] L~∞-Bounds of Solutions for Strongly Nonlinear Elliptic Problems with Two Lower Order Terms
Youssef Akdim
Mohammed Belayachi
Mostafa El Moumni
AnalysisinTheoryandApplications, 2017, 33 (01) : 46 - 58
[24] Removable sets for Holder continuous solutions of quasilinear elliptic equations with lower order terms
Ono, Takayori
MATHEMATISCHE ANNALEN, 2013, 356 (01) : 355 - 372
[25] Regularity theory and Green's function for elliptic equations with lower order terms in unbounded domains
Mourgoglou, Mihalis
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2023, 62 (09)
[26] Regularity theory and Green’s function for elliptic equations with lower order terms in unbounded domains
Mihalis Mourgoglou
Calculus of Variations and Partial Differential Equations, 2023, 62
[27] BOUNDEDNESS AND BLOWUP SOLUTIONS FOR QUASILINEAR PARABOLIC SYSTEMS WITH LOWER ORDER TERMS
Chen, Shaohua
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (02) : 587 - 600
[28] Local Holder continuity of weak solutions for an anisotropic elliptic equation
Di Castro, Agnese
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2013, 20 (03): : 463 - 486
[29] LINEAR ELLIPTIC EQUATIONS WITH LOWER-ORDER TERMS
Giannetti, Flavia
Greco, Luigi
Moscariello, Gioconda
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2013, 26 (5-6) : 623 - 638
[30] ON A CLASS OF NONLINEAR ELLIPTIC EQUATIONS WITH LOWER ORDER TERMS
Alvino, A.
Mercaldo, A.
Volpicelli, R.
Betta, M. F.
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2019, 32 (3-4) : 223 - 232

← 1 2 3 4 5 →