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
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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, 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: |
05 Dec 2022 14:55 |
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 |
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