Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations

An overview on flows of vector fields and on optimal transport.- Maximal regular flows for non-smooth vector fields.- Main properties of maximal regular flows and analysis of blow-up.- Lagrangian structure of transport equations.- The continuity equation with an integrable damping term.-  Regularity results for very degenerate elliptic equations.- An excess-decay result for a class of degenerate e...