A note on the engulfing property and the $\Gamma ^{1+ \alpha }$-regularity of convex functions in Carnot groups

DOI10.1090/S0002-9939-06-08359-6zbMath1109.35028OpenAlexW1493161316MaRDI QIDQ3419895

Diego Maldonado, Luca Capogna

Publication date: 1 February 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-06-08359-6

zbMATH Keywords

Monge-Ampère equationdoubling propertyFolland-Stein class

Mathematics Subject Classification ID

Related Items (8)

On the ${\mathbb H}$-cone-functions for H-convex sets ⋮ On proving 𝐶^{1,𝛼}_{𝑙𝑜𝑐}-estimates for convex functions ⋮ The engulfing property for sections of convex functions on the Heisenberg group and the associated quasi-distance ⋮ Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group ⋮ Regularity properties of \(H\)-convex sets ⋮ The engulfing property from a convex analysis viewpoint ⋮ Lifting of convex functions on Carnot groups and lack of convexity for a gauge function ⋮ A new characterization of convexity in free Carnot groups

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