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On the energy of a flow arising in shape optimization

Abstract : 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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Submitted on : Tuesday, July 11, 2006 - 11:35:38 AM
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Pierre Cardaliaguet, Olivier Ley. On the energy of a flow arising in shape optimization. Interfaces Free Bound., 2008, 10 (2), pp.223-243. ⟨hal-00084972⟩



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