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Curves and Gradients in Metric Spaces

Part of the Lectures in Mathematics ETH Zürich book series (LM)

Abstract

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 [20]); the last one deals with curves of maximal slope.

Keywords

Banach Space Lower Semicontinuous Chain Rule Maximal Slope Continuous Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2008

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