Holder continuity for nonlinear sub-elliptic systems with sub-quadratic growth

被引：0
|
作者：
Wang, Jialin [1 ]
Liao, Dongni [1 ]
Guo, Zhenhua [1 ]
Yu, Zefeng [1 ]
Wu, Shimin [2 ]
机构：
[1] Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Jiangxi, Peoples R China
[2] Gannan Normal Univ, Sch Phys & Elect Informat Technol, Ganzhou 341000, Jiangxi, Peoples R China
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2015年 / 109卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Partial regularity; Nonlinear sub-elliptic systems; Hormander's vector fields; Sub-quadratic natural growth condition; A-harmonic approximation technique; INTERIOR PARTIAL REGULARITY; QUASI-LINEAR EQUATIONS; MINIMIZERS; INTEGRALS; OPERATORS;
D O I：
10.1007/s13398-014-0162-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper is concerned with partial regularity of weak solutions to nonlinear sub-elliptic systems under sub-quadratic natural growth conditions. We begin with establishing a Sobolev-Poincare type inequality associated with Hormander's vector fields for u is an element of HW1-m (Omega, R-N) with 1 < m < 2. Then A-harmonic approximation method is applied, and partial Holder continuity with optimal local Holder exponent for gradients of weak solutions to the systems is established.
引用
收藏
页码：27 / 42
页数：16
相关论文
共 50 条
  • [1] Hölder continuity for nonlinear sub-elliptic systems with sub-quadratic growth
    Jialin Wang
    Dongni Liao
    Zhenhua Guo
    Zefeng Yu
    Shimin Wu
    Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2015, 109 : 27 - 42
  • [2] Holder Continuity for Sub-Elliptic Systems Under the Sub-Quadratic Controllable Growth in Carnot Groups
    Wang, Jialin
    Liao, Dongni
    Yu, Zefeng
    RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, 2013, 130 : 169 - 202
  • [3] Gradient regularity for nonlinear sub-elliptic systems with the drift term: sub-quadratic growth case
    Chen, Beibei
    Wang, Jialin
    Liao, Dongni
    AIMS MATHEMATICS, 2025, 10 (01): : 1407 - 1437
  • [4] Optimal partial regularity for sub-elliptic systems with sub-quadratic growth in Carnot groups
    Wang, Jialin
    Liao, Dongni
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (04) : 2499 - 2519
  • [5] Partial Holder continuity for nonlinear sub-elliptic systems with VMO-coefficients in the Heisenberg group
    Wang, Jialin
    Manfredi, Juan J.
    ADVANCES IN NONLINEAR ANALYSIS, 2018, 7 (01) : 97 - 116
  • [6] Regularity for sub-elliptic systems with VMO-coefficients in the Heisenberg group: the sub-quadratic structure case
    Wang, Jialin
    Zhu, Maochun
    Gao, Shujin
    Liao, Dongni
    ADVANCES IN NONLINEAR ANALYSIS, 2021, 10 (01) : 420 - 449
  • [7] Partial interior regularity for sub-elliptic systems with Dini continuous coefficients in Carnot groups: the sub-quadratic controllable case
    Liao, Dongni
    Wang, Jialin
    Yang, Qiang
    Wu, Shimin
    BOUNDARY VALUE PROBLEMS, 2017,
  • [8] Partial interior regularity for sub-elliptic systems with Dini continuous coefficients in Carnot groups: the sub-quadratic controllable case
    Dongni Liao
    Jialin Wang
    Qiang Yang
    Shimin Wu
    Boundary Value Problems, 2017
  • [9] Optimal partial regularity for nonlinear sub-elliptic systems
    Chen, Shuhong
    Tan, Zhong
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 387 (01) : 166 - 180
  • [10] Markovian Quadratic BSDEs with an Unbounded Sub-quadratic Growth
    Ju, Jingnan
    Tang, Shanjian
    CHINESE ANNALS OF MATHEMATICS SERIES B, 2024, 45 (03) : 441 - 462
12345