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

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

2003-09-09

arxiv.org/abs/math/0309167v1

Mathematics

Analysis of PDEs

Scientific paper

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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