Horizontal semiconcavity for the square of Carnot-Carathéodory distance on ideal Carnot groups and applications to Hamilton-Jacobi equations
Abstract
We show that the square of Carnot-Carathéodory 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2024
- DOI:
- 10.48550/arXiv.2402.19164
- arXiv:
- arXiv:2402.19164
- Bibcode:
- 2024arXiv240219164D
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35R03;
- 35D40;
- 49L25