Curves and Gradients in Metric Spaces
As we briefly discussed in the introduction, the notion of gradient flows in a metric space Open image in new window relies on two elementary but basic concepts: the metric derivative of an absolutely continuous curve with values in Open image in new window and the upper gradients of a functional defined in Open image in new window . The related definitions are presented in the next two sections (a more detailed treatment of this topic can be found for instance in ); the last one deals with curves of maximal slope.
KeywordsBanach Space Lower Semicontinuous Chain Rule Maximal Slope Continuous Curf
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