說明 
xxiii, 269 pages : illustrations, digital ; 24 cm 
系列 
Tesi ; 22 
附註 
An overview on flows of vector fields and on optimal transport  Maximal regular flows for nonsmooth vector fields  Main properties of maximal regular flows and analysis of blowup  Lagrangian structure of transport equations  The continuity equation with an integrable damping term  Regularity results for very degenerate elliptic equations  An excessdecay result for a class of degenerate elliptic equations  The VlasovPoisson system  The semigeostrophic system 

The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the VlasovPoisson system, which describes the evolution of a system of particles under the selfinduced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of largescale oceanic/atmospheric flows 
主題 
Vector fields


Elliptic functions


Mathematics


Partial Differential Equations


Calculus of Variations and Optimal Control; Optimization


Geophysics and Environmental Physics

