On the p-Laplacian evolution equation in metric measure spaces

The p-Laplacian evolution equation in metric measure spaces has been studied as the gradient flow L2 of p-Cheeger energy (for 1<p<∞). In this paper, using first-order differential structure on a space introduced by Gigli, we characterise subdifferential energy. This gives rise to new definition operator spaces, which allows us work with more detail. way, introduce notion solutions spaces. For p=1, obtain Green-Gauss formula similar one Anzellotti for Euclidean and use it 1-Laplacian study total variation flow. We also asymptotic behaviour equation, showing that 1≤p<2 have finite extinction time.