Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

被引：8

作者：

Balogh, Zoltan M. ^{[1
]}

Calogero, Andrea ^{[2
]}

Kristaly, Alexandru ^{[3
,4
]}

机构：

[1] Univ Bern, Math Inst, CH-3012 Bern, Switzerland

[2] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy

[3] Univ Babes Bolyai, Dept Econ, Cluj Napoca 400591, Romania

[4] Obuda Univ, Inst Appl Math, Budapest, Hungary

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2015年 / 269卷 / 09期

基金：

瑞士国家科学基金会;

关键词：

Heisenberg group; H-convex functions; Comparison principle; Aleksandrov-type maximum principle; MONGE-AMPERE EQUATION; CONVEX-FUNCTIONS; CARNOT GROUPS; HESSIAN MEASURES; REGULARITY; THEOREM;

D O I：

10.1016/j.jfa.2015.08.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we solve a problem raised by Gutierrez and Montanari about comparison principles for H-convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H-convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：2669 / 2708

页数：40

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[2]

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[3]

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

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