Uniform ball property and existence of optimal shapes for a wide class of geometric functionals - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2016

Uniform ball property and existence of optimal shapes for a wide class of geometric functionals

Jeremy Dalphin

Résumé

In this paper, we are interested in shape optimization problems involving the geometry (normal, curvatures) of the surfaces. We consider a class of hypersurfaces in R n satisfying a uniform ball condition and we prove the existence of a C 1,1-regular minimizer for general geometric functionals and constraints involving the rst-and second-order properties of surfaces, such as in R 3 problems of the form: inf ∂Ω j0 [x, n (x)] dA (x) + ∂Ω j1 [x, n (x) , H (x)] dA (x) + ∂Ω j2 [x, n (x) , K (x)] dA (x) , where n, H, and K respectively denotes the normal, the scalar mean curvature and the Gaussian curvature. We gives some various applications in the modelling of red blood cells such as the Canham-Helfrich energy and the Willmore functional.
Fichier principal
Vignette du fichier
epsilon_ball_geometry.pdf (805.73 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01136792 , version 1 (16-04-2015)
hal-01136792 , version 2 (04-02-2017)

Identifiants

Citer

Jeremy Dalphin. Uniform ball property and existence of optimal shapes for a wide class of geometric functionals. 2016. ⟨hal-01136792v2⟩
126 Consultations
448 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More