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What is a good introduction in gradient flows in metric spaces? I know the book Gradient flows: in metric spaces and in the space of probability measures by Luigi Ambrosio, Nicola Gigli and Giuseppe ...

This question may be posed somewhat vaguely, but I'm interested to actually get an idea of what to expect, so I try to not target it at a specific result. Assume that $G$ is a compact Lie group, ...

For a convex lower-semicontinuous functional on a Hilbert space $I\colon H\rightarrow\mathbb{R}$, it is shown in Evans' PDE that the Hilbert-space-valued ODE $$\begin{cases}\mathbf{u}'(t)\in-\partial ...