Calculus of Variations and Geometric Measure Theory

F. Dragoni - Q. Liu - Y. Zhang

Horizontal semiconcavity for the square of Carnot-Carath\'eodory distance on ideal Carnot groups and applications to Hamilton-Jacobi equations

created by dragoni on 29 Feb 2024

[BibTeX]

Preprint

Inserted: 29 feb 2024
Last Updated: 29 feb 2024

Year: 2024

Abstract:

We show that the square of Carnot-Carath'eodory distance from the origin, in ideal Carnot groups, enjoys the horizontal semiconcavity (h-semiconcavity) everywhere in the group including the origin. We apply this property to show h-semiconcavity for the solutions of a class of non-coercive evolutive Hamilton-Jacobi equations, by using the associated Hopf-Lax solutions.


Download: