Titre :

Strong approximation in h-mass of rectifiable currents under homological constraint

Auteur(s) :

Chambolle, Antonin [Auteur]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Ferrari, Luca Alberto Davide [Auteur]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Merlet, Benoît [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]

Titre de la revue :

Advances in Calculus of Variation

Pagination :

343--363

Éditeur :

Walter de Gruyter GmbH

Date de publication :

2021-07-01

ISSN :

1864-8266

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse fonctionnelle [math.FA]
Mathématiques [math]/Optimisation et contrôle [math.OC]

Résumé en anglais : [en]

Let h : R → R+ be a lower semi-continuous subbadditive and even function such that h(0) = 0 and h(θ) ≥ α|θ| for some α > 0. The h-mass of a k-polyhedral chain P =∑j θjσj in R n (0 ≤ k ≤ n) is defined as M h (P) := j h(θj) ...
Lire la suite >Let h : R → R+ be a lower semi-continuous subbadditive and even function such that h(0) = 0 and h(θ) ≥ α|θ| for some α > 0. The h-mass of a k-polyhedral chain P =∑j θjσj in R n (0 ≤ k ≤ n) is defined as M h (P) := j h(θj) H k (σj). If T = τ (M, θ, ξ) is a k-rectifiable chain, the definition extends to M h (T) := M h(θ) dH k. Given such a rectifiable flat chain T with M h (T) < ∞ and ∂T polyhedral, we prove that for every η > 0, it decomposes as T = P + ∂V with P polyhedral, V rectifiable, M h (V) < η and M h (P) < M h (T) + η. In short, we have a polyhedral chain P which strongly approximates T in h-mass and preserves the homological constraint ∂P = ∂T. These results are motivated by the study of approximations of M h by smoother functionals but they also provide explicit formulas for the lower semicontinuous envelope of T → M h (T) + I ∂S (∂T) with respect to the topology of the flat norm.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL