Harnack's inequality for a class of non-divergent equations in the Heisenberg group

被引：8

作者：

Abedin, Farhan ^{[1
]}

Gutierrez, Cristian E. ^{[1
]}

Tralli, Giulio ^{[2
]}

机构：

[1] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

[2] Sapienza Univ Roma, Dipartimento Matemat, Rome, Italy

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2017年 / 42卷 / 10期

基金：

美国国家科学基金会;

关键词：

Apriori estimates; subelliptic equations; symplectic matrices; CARNOT GROUPS; FORM; PRINCIPLES; MAXIMUM;

D O I：

10.1080/03605302.2017.1384836

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove an invariant Harnack's inequality for operators in non-divergence form structured on Heisenberg vector fields when the coecient matrix is uniformly positive definite, continuous, and symplectic. The method consists in constructing appropriate barriers to obtain pointwise-to-measure estimates for supersolutions in small balls, and then invoking the axiomatic approach developed by Di Fazio, Gutierrez, and Lanconelli to obtain Harnack's inequality.

引用

页码：1644 / 1658

页数：15

共 27 条

[1]

[Anonymous], 2010, Nonlinear partial differential equations and related topics

[2]

[Anonymous], 1989, ANN MATH STUDIES

[3] Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group [J].