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.

Balogh, Z., Calogero, A., Kristály, A. (2015). Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group. JOURNAL OF FUNCTIONAL ANALYSIS, 269(9), 2669-2708 [10.1016/j.jfa.2015.08.014].

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

CALOGERO, ANDREA GIOVANNI
Secondo
;
2015

Abstract

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.
Articolo in rivista - Articolo scientifico
Aleksandrov-type maximum principle; Comparison principle; H-convex functions; Heisenberg group; Analysis
English
2669
2708
40
Balogh, Z., Calogero, A., Kristály, A. (2015). Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group. JOURNAL OF FUNCTIONAL ANALYSIS, 269(9), 2669-2708 [10.1016/j.jfa.2015.08.014].
Balogh, Z; Calogero, A; Kristály, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/101284
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