Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations

Focusing on advanced mathematical concepts, the book first explores the transport equation for vector fields, emphasizing the Lagrangian structure and the regularity of solutions to degenerate elliptic equations related to transport models with congestion. The second part delves into the Lagrangian structure of solutions for the Vlasov-Poisson system, which models particle evolution influenced by gravitational and electrostatic fields, and examines the existence of solutions for the semigeostrophic system used in meteorology to analyze large-scale oceanic and atmospheric flows.