On the energy of a flow arising in shape optimization

Details On the energy of a flow arising in shape optimization On the energy of a flow arising in shape optimization

2006-07-11

arxiv.org/abs/math/0607255v1

Interfaces Free Bound. 10, 2 (2008) 223-243

Mathematics

Analysis of PDEs

Scientific paper

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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