关于以optimization形状出现的流动的能量
On the energy of a flow arising in shape optimization
摘要：
在Cardaliaguet-Ley（2006）中，我们定义了外伯努利自由边界问题梯度流的黏性解。我们证明了伴随能量沿流动方向不减。这证明了“梯度流”方法对此类问题的合理性。这个证明依赖于一个离散梯度流的构造，在Almart-Taylor-Wang（1993）的风格，并证明它收敛到黏性解。
英文摘要：
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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