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On the energy of a flow arising in shape optimization

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Date
2008
Link to item file
http://arxiv.org/abs/math/0607255v1
Dewey
Analyse
Sujet
exterior Bernoulli free boundary; viscosity solutions; Optimization
Journal issue
Interfaces and free boundaries
Volume
10
Number
2
Publication date
2008
Article pages
223-243
Publisher
European Mathematical Society
DOI
http://dx.doi.org/10.4171/IFB/187
URI
https://basepub.dauphine.fr/handle/123456789/6928
Collections
  • CEREMADE : Publications
Metadata
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Author
Cardaliaguet, Pierre
Ley, Olivier
Type
Article accepté pour publication ou publié
Abstract (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.

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