Semiconcavity, viscosity solutions and the square distance in Carnot groups

Dragoni, Federica ORCID: https://orcid.org/0000-0001-6076-9725 2026. Semiconcavity, viscosity solutions and the square distance in Carnot groups. Presented at: 2024 GAP Center Summer School, Ghent, November 2024. Published in: Chatzakou, Marianna, Ruzhansky, Michael and Van Bockstal, Karel eds. Direct and Inverse Problems with Applications: Extended Abstracts of the 2024 GAP Center Summer School. Trends in Mathematics Birkhäuser Cham, pp. 49-56. 10.1007/978-3-031-98645-1_5

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Abstract

We give an overview of 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-Carathéodory distance is h-semiconcave in step 2 Carnot groups.

Item Type:	Conference or Workshop Item - published (Other)
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Birkhäuser Cham
ISBN:	9783031986444
Last Modified:	13 Jan 2026 09:30
URI:	https://orca.cardiff.ac.uk/id/eprint/183820

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