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On the energy of a flow arising in shape optimization

Cardaliaguet, Pierre; Ley, Olivier (2008), On the energy of a flow arising in shape optimization, Interfaces and free boundaries, 10, 2, p. 223-243. http://dx.doi.org/10.4171/IFB/187

Type
Article accepté pour publication ou publié
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http://arxiv.org/abs/math/0607255v1
Date
2008
Nom de la revue
Interfaces and free boundaries
Volume
10
Numéro
2
Éditeur
European Mathematical Society
Pages
223-243
Identifiant publication
Métadonnées
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Auteur(s)
Cardaliaguet, Pierre
Ley, Olivier
Résumé (EN)
In Cardaliaguet-Ley (2006) we have defined a viscosity solution for the gradient flow of the exterior Bernoulli free boundary problem. We prove here that the associated energy is non decreasing along the flow. This justifies the "gradient flow" approach for such kind of problem. The proof relies on the construction of a discrete gradient flow in the flavour of Almgren-Taylor-Wang (1993) and on proving it converges to the viscosity solution.
Mots-clés
exterior Bernoulli free boundary; viscosity solutions; Optimization