English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We derive necessary optimality conditions for minimizers of regularfunctionals in the calculus of variations under smooth state constraints. Inthe literature, this classical problem is widely investigated. The novelty ofour result lies in the fact that the presence of state constraints enters theEuler-Lagrange equations as a local feedback, which allows to derive the$C^{1,1}$-smoothness of solutions. As an application, we discuss a constrainedMean Field Games problem, for which our optimality conditions allow toconstruct Lipschitz relaxed solutions, thus improving the existence result in[Cannarsa, P., Capuani, R., \textsl{Existence and uniqueness for Mean FieldGames with state constraints}, arXiv:1711.01063].

$\bf{C^{1,1}}$-smoothness of constrained solutions in the calculus of variations with application to mean field games