On the second order derivatives of convex functions on the Heisenberg group

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In the Euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous H-convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives for the class of continuous H-convex functions in the Heisenberg group.

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Analysis of PDEs, 35B50; 35B45; 35H20

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http://salesiana.dossiersoluciones.com/handle/123456789/68523

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0309167
 http://arxiv.org/abs/math/0309167

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arXiv