Critical points of solutions of sub-elliptic equations on the Heisenberg group

被引：0
|
作者：
Liu, Hairong [1 ]
Wu, Hui [2 ]
机构：
[1] Nanjing Forestry Univ, Sch Sci, Nanjing 210037, Peoples R China
[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 494卷 / 01期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Critical point; Star-shaped domain; Heisenberg group; Green function; CRITICAL SETS;
D O I：
10.1016/j.jmaa.2020.124579
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper concerns the critical points of a class of degenerate elliptic operators. We prove that the nonexistence of critical point of the Green function for the Kohn-Laplacian of an H-star-shaped region on the first Heisenberg group. Moreover, we prove that solutions to a class of semi-linear degenerate elliptic equations on an H-star-shaped ring have no critical point. (C) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页数：9
相关论文
共 50 条
  • [21] Gradient regularity for elliptic equations in the Heisenberg group
    Mingione, Giuseppe
    Zatorska-Goldstein, Anna
    Zhong, Xiao
    ADVANCES IN MATHEMATICS, 2009, 222 (01) : 62 - 129
  • [22] Critical semilinear equations on the Heisenberg group
    Lanconelli E.
    Annali dell’Università di Ferrara, 1999, 45 (1): : 187 - 195
  • [23] CRITICAL POINTS OF SOLUTIONS TO A KIND OF LINEAR ELLIPTIC EQUATIONS IN MULTIPLY CONNECTED DOMAINS
    Deng, Haiyun
    Liu, Hairong
    Yang, Xiaoping
    ISRAEL JOURNAL OF MATHEMATICS, 2022, 249 (02) : 935 - 971
  • [24] Bounded Solutions for a Class of Semilinear Equations on the Heisenberg Group
    Selmi, Imen
    POTENTIAL ANALYSIS, 2015, 42 (02) : 365 - 381
  • [25] Bounded Solutions for a Class of Semilinear Equations on the Heisenberg Group
    Imen Selmi
    Potential Analysis, 2015, 42 : 365 - 381
  • [26] Normalized solutions for critical Choquard equations involving logarithmic nonlinearity in the Heisenberg group
    Liang, Sihua
    Zheng, Xuechun
    Guo, Lifeng
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2025, 48 (03) : 3966 - 3978
  • [27] Critical Kirchhoff equations involving the p-sub-Laplacians operators on the Heisenberg group
    Sun, Xueqi
    Song, Yueqiang
    Liang, Sihua
    Zhang, Binlin
    BULLETIN OF MATHEMATICAL SCIENCES, 2023, 13 (02)
  • [28] PARTIAL SCHAUDER ESTIMATES FOR A SUB-ELLIPTIC EQUATION
    魏娜
    蒋永生
    吴永洪
    Acta Mathematica Scientia(English Series), 2016, 36 (03) : 945 - 956
  • [29] Multiple solutions of semilinear elliptic systems on the Heisenberg group
    Gao Jia
    Long-jie Zhang
    Jie Chen
    Boundary Value Problems, 2013
  • [30] Multiple solutions of semilinear elliptic systems on the Heisenberg group
    Jia, Gao
    Zhang, Long-jie
    Chen, Jie
    BOUNDARY VALUE PROBLEMS, 2013,
12345