Semiconcavity, viscosity solutions and the square distance in Carnot groups.

Dragoni, Federica ORCID: https://orcid.org/0000-0001-6076-9725 2024. Semiconcavity, viscosity solutions and the square distance in Carnot groups. Presented at: Summer School Workshop IV, Ghent, November 2024.

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Abstract

We give an overview on semiconcavity, starting from the standard notion, up to more recent generalizations in a different geometrical context, such as Carnot groups; focusing in particular on the viscosity characterization by bounds for second derivatives. We then apply these theories to show some recent results obtained by the author, in collaboration with Qing Liu and Ye Zhang. In particular we show that the square Carnot-Carath\'eodory distance is h-semiconcave in step 2 Carnot groups.

Item Type:	Conference or Workshop Item (Lecture)
Status:	Unpublished
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Last Modified:	14 Jan 2025 17:00
URI:	https://orca.cardiff.ac.uk/id/eprint/174867

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