Global gradient estimates for the p(•)-Laplacian

被引：45
|
作者：
Diening, L.
Schwarzacher, S.
机构：
[1] Theresienstr. 39
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2014年 / 106卷
关键词：
Nonlinear Calderon-Zygmund theory; Variable exponents; Generalized Lebesgue and Sobolev spaces; Electrorheological fluids; MAXIMAL-FUNCTION; SPACES; INTEGRABILITY; FUNCTIONALS; REGULARITY; OPERATORS;
D O I：
10.1016/j.na.2014.04.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider Calderon-Zygmund type estimates for the non-homogeneous p(center dot)-Laplacian system -div(| Du|(p(center dot)-2Du)) = -div(| G|(p(center dot)-2)G), where p is a variable exponent. We show that |G| p(center dot)epsilon L-q(R-n) boolean AND L-1(R-n) implies |Du|(p(center dot)) epsilon L-q(R-n) boolean AND L-1(R-n) for any q >= 1. We also prove local estimates independent of the size of the domain and introduce new techniques to variable analysis. The paper is an extension of the local estimates of Acerbi-Mingione (2005). (C) 2014 Elsevier Ltd. All rights reserved.
引用
收藏
页码：70 / 85
页数：16
相关论文
共 50 条
  • [1] Global gradient estimates for the parabolic p(x, t)-Laplacian equation
    Zhang, Chao
    Zhou, Shulin
    Xue, Xiaoping
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 105 : 86 - 101
  • [2] GLOBAL GRADIENT ESTIMATES FOR THE p(x)-LAPLACIAN EQUATIONS WITH THE LOGARITHMIC FUNCTION IN Rn
    Ma, Rumeng
    Yao, Fengping
    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2023, 24 (11) : 2473 - 2488
  • [3] Global gradient estimates for asymptotically regular problems of p(x)-Laplacian type
    Byun, Sun-Sig
    Oh, Jehan
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2018, 20 (08)
  • [4] Global gradient estimates for elliptic equations of p(x)-Laplacian type with BMO nonlinearity
    Byun, Sun-Sig
    Ok, Jihoon
    Ryu, Seungjin
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2016, 715 : 1 - 38
  • [5] Gradient estimates for the p(x)-Laplacian equation in RN
    Zhang, Chao
    Zhou, Shulin
    Ge, Bin
    ANNALES POLONICI MATHEMATICI, 2015, 114 (01) : 45 - 65
  • [6] A note on gradient estimates for p-Laplacian equations
    Guarnotta, Umberto
    Marano, Salvatore A.
    BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2024, 17 (02): : 391 - 399
  • [7] Weighted gradient estimates for the parabolic p-Laplacian equations
    Yao, Fengping
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 112 : 58 - 68
  • [8] LOCAL GRADIENT ESTIMATES FOR THE p(x)-LAPLACIAN ELLIPTIC EQUATIONS
    Yao, Fengping
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2014, 17 (01): : 259 - 268
  • [9] ON A GLOBAL GRADIENT ESTIMATE IN p-LAPLACIAN PROBLEMS
    Ercole, Grey
    ISRAEL JOURNAL OF MATHEMATICS, 2025, 265 (02) : 945 - 968
  • [10] Holder gradient estimates for parabolic homogeneous p-Laplacian equations
    Jin, Tianling
    Silvestre, Luis
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2017, 108 (01): : 63 - 87
12345