Some comparison, symmetry and monotonicity results for Carnot-Carathéodory spaces

Yuxin Ge; Dong Ye

doi:10.57262/ade/1357141501

Some comparison, symmetry and monotonicity results for Carnot-Carathéodory spaces

Yuxin Ge
, Dong Ye

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider here some differential operators arising from the so called Carnot-Carathéodory metric spaces associated with a family of vector fields X = (X₁, . . . ,X_k), which include the Hörmander type as a special case. We prove some weak and strong comparison results for solutions of the relevant differential inequalities. We then use these results to get some symmetry and monotonicity properties of solutions of the relevant partial differential equations.

Original language	English
Pages (from-to)	51-72
Number of pages	22
Journal	Advances in Differential Equations
Volume	6
Issue number	1
DOIs	https://doi.org/10.57262/ade/1357141501
State	Published - 2001
Externally published	Yes

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title = "Some comparison, symmetry and monotonicity results for Carnot-Carath{\'e}odory spaces",

abstract = "We consider here some differential operators arising from the so called Carnot-Carath{\'e}odory metric spaces associated with a family of vector fields X = (X1, . . . ,Xk), which include the H{\"o}rmander type as a special case. We prove some weak and strong comparison results for solutions of the relevant differential inequalities. We then use these results to get some symmetry and monotonicity properties of solutions of the relevant partial differential equations.",

author = "Yuxin Ge and Dong Ye",

year = "2001",

doi = "10.57262/ade/1357141501",

language = "英语",

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N2 - We consider here some differential operators arising from the so called Carnot-Carathéodory metric spaces associated with a family of vector fields X = (X1, . . . ,Xk), which include the Hörmander type as a special case. We prove some weak and strong comparison results for solutions of the relevant differential inequalities. We then use these results to get some symmetry and monotonicity properties of solutions of the relevant partial differential equations.

AB - We consider here some differential operators arising from the so called Carnot-Carathéodory metric spaces associated with a family of vector fields X = (X1, . . . ,Xk), which include the Hörmander type as a special case. We prove some weak and strong comparison results for solutions of the relevant differential inequalities. We then use these results to get some symmetry and monotonicity properties of solutions of the relevant partial differential equations.

UR - https://www.scopus.com/pages/publications/0005145723

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DO - 10.57262/ade/1357141501

M3 - 文章

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SN - 1079-9389

VL - 6

SP - 51

EP - 72

JO - Advances in Differential Equations

JF - Advances in Differential Equations

IS - 1

ER -

Some comparison, symmetry and monotonicity results for Carnot-Carathéodory spaces

Abstract

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