Maximum and comparison principles for convex functions on the Heisenberg group

被引：34

作者：

Gutiérrez, CE ^{[1
]}

Montanari, A

机构：

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

[2] Univ Bologna, Dipartmento Matemat, Bologna, Italy

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2004年 / 29卷 / 9-10期

基金：

美国国家科学基金会;

关键词：

convex functions on the Heisenberg group; null Lagrangian property; maximum principle; oscillation estimate; Monge-Ampere measures; comparison principle;

D O I：

10.1081/PDE-200037752

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove estimates, similar in form to the classical Aleksandrov estimates, for a Monge-Ampere type operator on the Heisenberg group. A notion of normal mapping does not seem to be available in this context and the method of proof uses integration by parts and oscillation estimates that lead to the construction of an analogue of Monge-Ampere measures for convex functions in the Heisenberg group.

引用

页码：1305 / 1334

页数：30

共 13 条

[1]

[Anonymous], 2001, MONGE AMPERE EQUATIO

[2]

Balogh ZM, 2003, ANN SCUOLA NORM-SCI, V2, P847

[3] On ∞-harmonic functions on the Heisenberg group [J].