Interfaces and Free Boundaries

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Volume 10, Issue 2, 2008, pp. 223–243
DOI: 10.4171/IFB/187

Published online: 2008-06-30

On the energy of a flow arising in shape optimization

Pierre Cardaliaguet[1] and Olivier Ley[2]

(1) Université de Bretagne Occidentale, Brest, France
(2) Université de Tours, France

In \cite{cl05} 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 increasing along the flow. For this we build a discrete gradient flow in the flavour of Almgren, Taylor and Wang \cite{atw93}.

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Cardaliaguet Pierre, Ley Olivier: On the energy of a flow arising in shape optimization. Interfaces Free Bound. 10 (2008), 223-243. doi: 10.4171/IFB/187