A new variational inequality in the calculus of variations and Lipschitz regularity of minimizers - Université de Bretagne Occidentale Access content directly
Journal Articles Journal of Differential Equations Year : 2020

A new variational inequality in the calculus of variations and Lipschitz regularity of minimizers

Abstract

We consider a nonautonomous problem of the calculus of variations where the Lagrangian is Borel measurable; we allow state, velocity and endpoint constraints. We prove that if the Lagrangian satisfies a nonsmooth version of Cesari's Condition (S), then any W^{1,1} local minimizer is Lipschitz whenever Λ is coercive. The proof is obtained via a new variational inequality, called also directional Weierstrass type condition, formulated here, that holds under the extended Condition (S) (just Borel measurability if Λ is autonomous). The proof of the directional Weierstrass type condition (W) is based on Clarke's nonsmooth recent versions of the Maximum Principle.
No file

Dates and versions

hal-04315945 , version 1 (30-11-2023)

Identifiers

Cite

Piernicola Bettiol, Carlo Mariconda. A new variational inequality in the calculus of variations and Lipschitz regularity of minimizers. Journal of Differential Equations, 2020, 268 (5), pp.2332-2367. ⟨10.1016/j.jde.2019.09.011⟩. ⟨hal-04315945⟩
5 View
0 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More