Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations With Applications to the Vlasov-Poisson and Semigeostrophic Systems /
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 congest...
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| Language: | English |
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Pisa :
Scuola Normale Superiore : Imprint: Edizioni della Normale,
2017.
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| Edition: | 1st ed. 2017. |
| Series: | Theses (Scuola Normale Superiore),
22 |
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| Online Access: | https://doi.org/10.1007/978-88-7642-607-0 |
Table of Contents:
- 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 elliptic equations
- The Vlasov-Poisson system
- The semigeostrophic system. .