Preprint

Inserted: 19 dec 2025
Last Updated: 19 dec 2025

Year: 2025

Abstract:

This document contains additional proofs to the section 4.3. of the article published in 2024 in J. Convex Anal. 31, No. 2 (p 619-670).\\ Indeed, in an interesting discussion with Giulia Cavagnari, she made me realize %that it should have been wise to add the proof of the remark 4.26. Moreover, %she noticed, that the second part of Proposition 4.27. (that is $V_L$ is a supersolution), proved with the only help of the dynamic programming principle, (given in remark 4.26.) is not obvious at all. Indeed, as she mentioned, for some $X$, $V_L(t_0,X)$ might have no optimal trajectories. She is quite right and a lemma will be added in the present document to avoid this difficulty. I will also provide the proof of remark 4.26. which is not included in the orignal document

Download:

• Addendum-EquivalenceExtension.pdf