一类p-Laplacian方程解的存在性与对称性研究

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 725-734.

一类p-Laplacian方程解的存在性与对称性研究

钱红丽,黄小涛*()

^{南京航空航天大学数学系南京 211106}

收稿日期:2019-06-11 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 黄小涛 E-mail:huang2008@hotmail.com
基金资助:
南京航空航天大学青年科技创新基金(NS2019044);南京航空航天大学研究生创新基地（实验室）开放基金(KFJJ20180803)

A Symmetry Result for a Class of p-Laplace Involving Baouendi-Grushin Operators via Constrained Minimization Method

Hongli Qian,Xiaotao Huang*()

^{Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211016}

Received:2019-06-11 Online:2020-06-26 Published:2020-07-15
Contact: Xiaotao Huang E-mail:huang2008@hotmail.com
Supported by:
the Nanjing University of Aeronautics and Astronautics Youth Technology Innovation Fund(NS2019044);the Foundation of the Graduate Innovation Center, Nanjing University of Aeronautics and Astronautics(KFJJ20180803)

摘要/Abstract

摘要：

该文研究一类含Baouendi-Grushin算子的p-Laplace方程解的存在性与对称性问题.通过重排方程对应的极小化约束泛函，得到此泛函关于某点中心对称的最小极值，从而获得方程正解的一些存在性和对称性结果.此结论推广了经典p-Laplace方程和Baouendi-Grushin型Laplace方程的相关结果.

关键词: p-Laplace方程, Baouendi-Grushin算子, 存在性和对称性, 重排, 约束最小化方法

Abstract:

The purpose of this paper is to investigate a spacial p-Laplace equation involving Baouendi-Grushin operators. Some existence and symmetry results for positive solutions are obtained by rearrangement of its corresponding constrained minimization. These results are in accordance with those for the classical p-Laplace equations and the Baouendi-Grushin type sub-Laplacian equations.

Key words: p-Laplace equations, Baouendi-Grushin operators, Existence and symmetry, rearrangement, Constrained minimization method

中图分类号:

O175.5

钱红丽,黄小涛. 一类p-Laplacian方程解的存在性与对称性研究[J]. 数学物理学报, 2020, 40(3): 725-734.

Hongli Qian,Xiaotao Huang. A Symmetry Result for a Class of p-Laplace Involving Baouendi-Grushin Operators via Constrained Minimization Method[J]. Acta mathematica scientia,Series A, 2020, 40(3): 725-734.

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