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

Balogh, Zoltan; Calogero, Andrea; Kristaly, Alexandru (2015). Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group. Journal of functional analysis, 269(9), pp. 2669-2708. Elsevier 10.1016/j.jfa.2015.08.014

[img]
Preview
Text
1305.5638.pdf - Accepted Version
Available under License Creative Commons: Attribution-Noncommercial-No Derivative Works (CC-BY-NC-ND).

Download (369kB) | Preview
[img] Text
1-s2.0-S0022123615003304-main.pdf - Published Version
Restricted to registered users only
Available under License Publisher holds Copyright.

Download (655kB) | Request a copy

In this paper we solve a problem raised by Gutiérrez 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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Balogh, Zoltan and Kristaly, Alexandru

Subjects:

500 Science > 510 Mathematics

ISSN:

0022-1236

Publisher:

Elsevier

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

08 Jun 2016 13:18

Last Modified:

30 Aug 2017 02:30

Publisher DOI:

10.1016/j.jfa.2015.08.014

ArXiv ID:

1305.5638v3

BORIS DOI:

10.7892/boris.81133

URI:

https://boris.unibe.ch/id/eprint/81133

Actions (login required)

Edit item Edit item
Provide Feedback