Gamma-convergence of gradient flows on Hilbert and metric spaces and applications
Gamma-convergence of gradient flows on Hilbert and metric spaces and applications
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DOI：
10.3934/dcds.2011.31.1427
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发表时间：
2011-09
影响因子：
1.1
通讯作者：
S. Serfaty
中科院分区：
文献类型：
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作者：
S. Serfaty
我们关心的是-收敛的梯度流，这是一个概念，以确保如果一个家庭的能源泛函依赖于一个参数-收敛，那么解决方案相关联的梯度流收敛以及。在本文中，我们提出了一个审查的抽象理论和它的应用，并推广计划的度量空间，没有出现在其他地方。我们还提到了开放的问题和前景。- 收敛是由De Giorgi在70年代提出的。它提供了一族能量泛函E”收敛到极限泛函F的一个方便的概念，特别是保证了E”的极小元收敛到F的极小元。在[DeG 1]中，De Giorgi提出了一个问题，即知道在解之间是否存在任何一般关系。
We are concerned with -convergence of gradient ows, which is a notion meant to ensure that if a family of energy functionals depending of a parameter -converges, then the solutions to the associated gradient ows converge as well. In this paper we present both a review of the abstract \theory" and of the applications it has had, and a generalization of the scheme to metric spaces which has not appeared elsewhere. We also mention open problems and perspectives. -convergence was introduced by De Giorgi in the 70’s. It provides a convenient notion of convergence of a family of energy functionalsE" to a limiting functionalF , which ensures in particular that minimizers ofE" converge to minimizers ofF . In [DeG1], De Giorgi raised the question of knowing whether there was any general relation between solutions of the