Flows of Non-smooth Vector Fields and Degenerate Elliptic Equations

1. An overview on flows of vector fields and on optimal transport
Maria Colombo

2. Maximal regular flows for non-smooth vector fields
Maria Colombo

3. Main properties of maximal regular flows and analysis of blow-up
Maria Colombo

4. Lagrangian structure of transport equations
Maria Colombo

5. The continuity equation with an integrable damping term
Maria Colombo

6. Regularity results for very degenerate elliptic equations
Maria Colombo

7. An excess-decay result for a class of degenerate elliptic equations
Maria Colombo

8. The Vlasov-Poisson system
Maria Colombo

9. The semigeostrophic system
Maria Colombo

Keywords: Mathematics, Partial Differential Equations, Calculus of Variations and Optimal Control; Optimization, Geophysics and Environmental Physics