| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 87 | |
| Number of page(s) | 32 | |
| DOI | https://doi.org/10.1051/cocv/2023079 | |
| Published online | 18 December 2023 | |
A uniqueness result for a non-strictly convex problem in the calculus of variations
Institut de Mathématiques de Toulouse, CNRS UMR 5219 Université de Toulouse, F-31062 Toulouse Cedex 9, France
* Corresponding author: benjamin.lledos@math.univ-toulouse.fr
Received:
25
July
2023
Accepted:
4
November
2023
We prove the uniqueness of the solution for a non-strictly convex problem in the Calculus of Variations of the form ∫φ(∇v) − λv. Here, φ is a convex function not differentiable at the origin and λ is a Lipschitz function. To prove this result, we show that under fairly general assumptions the minimizers are globally Lipschitz continuous.
Mathematics Subject Classification: 35A02 / 49N99
Key words: Uniqueness in Calculus of Variations / Non-strictly convex problem / Global Lipschitz regularity / Regularity of boundary of level sets
© The authors. Published by EDP Sciences, SMAI 2023
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