Abstract
In Cardaliaguet-Ley (2006) we have defined a viscosity solution for the 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 in the flavour of Almgren-Taylor-Wang (1993) and on proving it converges to the viscosity solution.
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