Séminaire d’Analyse

Some results about uniqueness in the Calculus of Variations.

by Mr Benjamin Lledos (IMT)

Amphi Schwartz

Amphi Schwartz


We try to find a framework where we can prove uniqueness for non-strictly convex problems in the Calculus of Variations. The main idea is to generalize a method developed by Marcellini for a specific case. After studying some counterexamples and a simpler case, we prove the uniqueness for two problems. These results are based on the global Lipschitz regularity of the minimizers and on a good comprehension of the regularity of their level sets.