Calculus of Variations and Geometric Measure Theory

V. Magnani - M. Scienza

Regularity estimates for convex functions in Carnot-Carathéodory spaces

created by magnani on 14 Jun 2012
modified on 25 Dec 2020


Published Paper

Inserted: 14 jun 2012
Last Updated: 25 dec 2020

Journal: Rev. Mat. Iberoam.
Volume: 32
Number: 3
Pages: 835-858
Year: 2016


We prove some regularity estimates for a class of convex functions in Carnot-Carathéodory spaces, generated by Hörmander vector fields. Our approach relies on both the structure of metric balls induced by Hörmander vector fields and upper estimates for subsolutions of sub-Laplacians.

Keywords: convexity, Carnot-Carathéodory spaces, Lipschitz estimates, Hörmander condition