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Maximum and comparison principles for convex functions on the Heisenberg group

Gutiérrez, CE
; 
Montanari, A
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Journal Article
Date
2004-09-01
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Subject
convex functions on the Heisenberg group
 null Lagrangian property
 maximum principle
 oscillation estimate
 Monge-Ampere measures
 comparison principle
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http://hdl.handle.net/20.500.12613/6120
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0306059v1.pdf
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DOI
10.1081/PDE-200037752
Abstract
We prove estimates, similar in form to the classical Aleksandrov estimates, for a Monge-Ampère type operator on the Heisenberg group. A notion of normal mapping does not seem to be available in this context and the method of proof uses integration by parts and oscillation estimates that lead to the construction of an analogue of Monge-Ampère measures for convex functions in the Heisenberg group.
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Informa UK Limited
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Communications in Partial Differential Equations
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