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

页数：9

共 50 条

[1] The polynomial growth solutions to some sub-elliptic equations on the Heisenberg group
Liu, Hairong
Long, Tian
Yang, Xiaoping
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2019, 21 (01)
[2] EXISTENCE OF SOLUTION OF SUB-ELLIPTIC EQUATIONS ON THE HEISENBERG GROUP WITH CRITICAL GROWTH AND DOUBLE SINGULARITIES
Chen, Jianqing
Rocha, Eugenio M.
OPUSCULA MATHEMATICA, 2013, 33 (02) : 237 - 254
[3] Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations
Liu, Qing
Zhou, Xiaodan
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2021, 22 (04) : 2039 - 2076
[4] UNIVERSAL INEQUALITIES FOR EIGENVALUES OF A SYSTEM OF SUB-ELLIPTIC EQUATIONS ON HEISENBERG GROUP
Du, Feng
Wu, Chuanxi
Li, Guanghan
Xia, Changyu
KODAI MATHEMATICAL JOURNAL, 2015, 38 (02) : 437 - 450
[5] Comparison Principles for Some Fully Nonlinear Sub-Elliptic Equations on the Heisenberg Group
YanYan Li
Bo Wang
Analysis in Theory and Applications, 2019, 35 (03) : 312 - 334
[6] SEMI-LINEAR SUB-ELLIPTIC EQUATIONS ON THE HEISENBERG GROUP WITH A SINGULAR POTENTIAL
Mokrani, Houda
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (05) : 1619 - 1636
[7] The Moser-Trudinger inequality in unbounded domains of Heisenberg group and sub-elliptic equations
Cohn, William S.
Nguyen Lam
Lu, Guozhen
Yang, Yunyan
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (12) : 4483 - 4495
[8] Strong Unique Continuation of Sub-elliptic Operator on the Heisenberg Group
Hairong LIU
Xiaoping YANG
Chinese Annals of Mathematics(Series B), 2013, 34 (03) : 461 - 478
[9] Strong unique continuation of sub-elliptic operator on the Heisenberg group
Hairong Liu
Xiaoping Yang
Chinese Annals of Mathematics, Series B, 2013, 34 : 461 - 478
[10] Strong unique continuation of sub-elliptic operator on the Heisenberg Group
Liu, Hairong
Yang, Xiaoping
CHINESE ANNALS OF MATHEMATICS SERIES B, 2013, 34 (03) : 461 - 478

← 1 2 3 4 5 →