Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group
Data(s) |
2015
31/12/1969
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Resumo |
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. |
Formato |
application/pdf application/pdf |
Identificador |
http://boris.unibe.ch/81133/1/1305.5638.pdf http://boris.unibe.ch/81133/8/1-s2.0-S0022123615003304-main.pdf 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 <http://dx.doi.org/10.1016/j.jfa.2015.08.014> doi:10.7892/boris.81133 info:doi:10.1016/j.jfa.2015.08.014 urn:issn:0022-1236 |
Idioma(s) |
eng |
Publicador |
Elsevier |
Relação |
http://boris.unibe.ch/81133/ |
Direitos |
info:eu-repo/semantics/embargoedAccess info:eu-repo/semantics/restrictedAccess |
Fonte |
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 <http://dx.doi.org/10.1016/j.jfa.2015.08.014> |
Palavras-Chave | #510 Mathematics |
Tipo |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion PeerReviewed |