Maximum and comparison principles for convex functions on the Heisenberg group

Gutierrez CE; Montanari A

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Maximum and comparison principles for convex functions on the Heisenberg group

机译：海森堡群凸函数的最大值和比较原理

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摘要

We prove estimates, similar in form to the classical Aleksandrov estimates, for a Monge-Ampere 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-Ampere measures for convex functions in the Heisenberg group.

机译：我们证明了Heisenberg群上Monge-Ampere类型算子的估计，其形式与经典的Aleksandrov估计相似。在这种情况下，似乎没有法线贴图的概念，证明方法使用了部分积分和振动估计，从而为海森堡组的凸函数构造了蒙格-安培度量的类似物。

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来源
《Communications in Partial Differential Equations》 |2004年第10期|共30页
作者
Gutierrez CE; Montanari A;
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正文语种 eng
中图分类偏微分方程;
关键词
convex functions on the Heisenberg group; null Lagrangian property; maximum principle; oscillation estimate; Monge-Ampere measures; comparison principle;

机译：海森堡群上的凸函数;拉格朗日性质;最大原理;振动估计;Monge-Ampere测度;比较原理;

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Maximum and comparison principles for convex functions on the Heisenberg group

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