Gradient estimates for Stokes systems in domains

被引：0

作者：

Choi, Jongkeun ^{[1
]}

Dong, Hongjie ^{[1
]}

机构：

[1] Brown Univ, Div Appl Math, 182 George St, Providence, RI 02912 USA

来源：

DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS | 2019年 / 16卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Stokes system; Dini mean oscillation condition; C-1-estimate; weak type-(1,1)-estimate; C-1;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the stationary Stokes system with Dini mean oscillation coefficients in a domain having C-1,C-Dini boundary. We prove that if (u, p) is a weak solution of the system with zero Dirichlet boundary condition, then (Du,p) is continuous up to the boundary. We also prove a weak type-(1,1) estimate for (Du,p).

引用

页码：1 / 24

页数：24

共 50 条

[41] Weighted estimates for elliptic systems on Lipschitz domains
Shen, Zhongwei
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2006, 55 (03) : 1135 - 1154
[42] Classical solvability and uniform estimates for the steady Stokes system in domains with noncompact boundaries
Pileckas, K
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1996, 6 (02): : 149 - 167
[43] Resolvent estimates for the Stokes operator in bounded and exterior C1 domains
Geng, Jun
Shen, Zhongwei
MATHEMATISCHE ANNALEN, 2024,
[44] RESOLVENT ESTIMATES OF THE STOKES SYSTEM WITH NAVIER BOUNDARY CONDITIONS IN GENERAL UNBOUNDED DOMAINS
Farwig, Reinhard
Rosteck, Veronika
ADVANCES IN DIFFERENTIAL EQUATIONS, 2016, 21 (5-6) : 401 - 428
[45] Decay estimates for strong solutions of the Navier-Stokes equations in exterior domains
Wiegner M.
Annali dell’Università di Ferrara, 2000, 46 (1): : 61 - 79
[46] OPTIMAL BOUNDARY ESTIMATES FOR STOKES SYSTEMS IN HOMOGENIZATION THEORY
Gu, Shu
Xu, Qiang
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2017, 49 (05) : 3831 - 3853
[47] Global gradient estimates for general nonlinear parabolic equations in nonsmooth domains
Byun, Sun-Sig
Ok, Jihoon
Ryu, Seungjin
JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (11) : 4290 - 4326
[48] Addendum to the paper: Nonlinear gradient estimates for elliptic equations in quasiconvex domains
Sun-Sig Byun
Hun Kwon
Hyoungsuk So
Lihe Wang
Calculus of Variations and Partial Differential Equations, 2015, 54 : 1455 - 1455
[49] Gradient estimates for p-Laplacian equation in composite Reifenberg domains
Zhang, Chao
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 133 : 134 - 143
[50] GRADIENT ESTIMATES FOR A CLASS OF ELLIPTIC-SYSTEMS
LIEBERMAN, GM
ANNALI DI MATEMATICA PURA ED APPLICATA, 1993, 164 : 103 - 120

← 1 2 3 4 5 →