Quasilinear divergence form elliptic equations in rough domains

被引：6
作者：
Palagachev, Dian K. [1 ]
机构：
[1] Politecn Bari, Dipartimento Matemat, I-70125 Bari, Italy
来源：
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2010年 / 55卷 / 5-6期
关键词：
divergence form quasilinear elliptic equations; weak solvability; Holder regularity; a priori estimates; Reifenberg flat domain; BMO; COEFFICIENTS;
D O I：
10.1080/17476930903276159
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Existence and global Holder continuity are proved for the weak solution to the Dirichlet problem {div(a(ij)(x, u)D(j)u + a(t)(x, u)) = b(x, u, Du) in Omega subset of R(n), u = 0 on partial derivative Omega over Reifenberg flat domains Omega. The principal coefficients a(ij)(x, u) are discontinuous with respect to x with small BMO-norms and b(x, u, Du) grows as vertical bar Du vertical bar(r) with r < 1 + 2/n.
引用
收藏
页码：581 / 591
页数：11
相关论文
共 50 条
  • [31] Gradient estimates in generalized Orlicz spaces for quasilinear elliptic equations via extrapolation
    Wu, Ruimin
    Jiang, Yinsheng
    Wang, Liyuan
    [J]. AIMS MATHEMATICS, 2023, 8 (10): : 24153 - 24161
  • [32] A PRIORI ESTIMATES AND EXISTENCE FOR QUASILINEAR ELLIPTIC EQUATIONS WITH NONLINEAR NEUMANN BOUNDARY CONDITIONS
    Hu, Zhe
    Wang, Li
    Zhao, Peihao
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016,
  • [33] Regularity estimates for quasilinear elliptic equations with variable growth involving measure data
    Byun, Sun-Sig
    Ok, Jihoon
    Park, Jung-Tae
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2017, 34 (07): : 1639 - 1667
  • [34] Global weighted estimates for quasilinear elliptic equations with non-standard growth
    Zhang, Chao
    Zhou, Shulin
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 267 (02) : 605 - 642
  • [35] GLOBAL GRADIENT ESTIMATES FOR A GENERAL CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH ORLICZ GROWTH
    Baasandorj, Sumiya
    Byun, Sun-Sig
    Lee, Ho-Sik
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (10) : 4189 - 4206
  • [36] Weighted W1, p(•)-Regularity for Degenerate Elliptic Equations in Reifenberg Domains
    Zhang, Junqiang
    Yang, Dachun
    Yang, Sibei
    [J]. ADVANCES IN NONLINEAR ANALYSIS, 2022, 11 (01) : 535 - 579
  • [37] LORENTZ ESTIMATES FOR ASYMPTOTICALLY REGULAR ELLIPTIC EQUATIONS IN QUASICONVEX DOMAINS
    Zhang, Junjie
    Zheng, Shenzhou
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016,
  • [38] An L p -theory of Stochastic PDEs of Divergence Form on Lipschitz Domains
    Kim, Kyeong-Hun
    [J]. JOURNAL OF THEORETICAL PROBABILITY, 2009, 22 (01) : 220 - 238
  • [39] Regularity theory in Orlicz spaces for elliptic equations in Reifenberg domains
    Jia, Huilian
    Li, Dongsheng
    Wanga, Lihe
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 334 (02) : 804 - 817
  • [40] ELLIPTIC EQUATIONS WITH MATRIX WEIGHTS AND MEASURABLE NONLINEARITIES ON NONSMOOTH DOMAINS
    Byun, Sun-Sig
    Cho, Yumi
    Lee, Ho-Sik
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 152 (07) : 2963 - 2982
12345