Title :

Non-convex functionals penalizing simultaneous oscillations along independent directions: rigidity estimates

Author(s) :

Goldman, Michael [Auteur]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Merlet, Benoît [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]

Journal title :

Annali della Scuola Normale Superiore di Pisa, Classe di Scienze

Pages :

1473--1509

Publisher :

Scuola Normale Superiore

Publication date :

2021

ISSN :

0391-173X

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

We study a family of non-convex functionals {E} on the space of measurable functions u : Ω 1 × Ω 2 ⊂ R n 1 × R n 2 → R. These functionals vanish on the non-convex subset S(Ω 1 × Ω 2) formed by functions of the form u(x 1 ...
Show more >We study a family of non-convex functionals {E} on the space of measurable functions u : Ω 1 × Ω 2 ⊂ R n 1 × R n 2 → R. These functionals vanish on the non-convex subset S(Ω 1 × Ω 2) formed by functions of the form u(x 1 , x 2) = u 1 (x 1) or u(x 1 , x 2) = u 2 (x 2). We investigate under which conditions the converse implication "E(u) = 0 ⇒ u ∈ S(Ω 1 × Ω 2)" holds. In particular, we show that the answer depends strongly on the smoothness of u. We also obtain quantitative versions of this implication by proving that (at least for some parameters) E(u) controls in a strong sense the distance of u to S(Ω 1 × Ω 2).Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Optimisation de forme
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL