Estimates and regularity results for the DiPerna-Lions flow

@inproceedings{Crippa2008EstimatesAR,
  title={Estimates and regularity results for the DiPerna-Lions flow},
  author={Gianluca Crippa and Camillo De Lellis},
  year={2008}
}
Abstract In this paper we derive new simple estimates for ordinary differential equations with Sobolev coefficients. These estimates not only allow to recover some old and recent results in a simple direct way, but they also have some new interesting corollaries. 

A quantitative theory for the continuity equation

Support Theorem for Stochastic Differential Equations with Sobolev Coefficients

In this paper we prove a support theorem for stochastic differential equations with Sobolev coefficients in the framework of DiPerna-Lions theory.

Optimal stability estimates for continuity equations

  • Christian Seis
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2018
This review paper is concerned with the stability analysis of the continuity equation in the DiPerna–Lions setting in which the advecting velocity field is Sobolev regular. Quantitative estimates for

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The aim of this note is to prove sharp regularity estimates for solutions of the continuity equation associated to vector fields of class $W^{1,p}$ with $p>1$. The regularity is of "logarithmic

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Hydrodynamics and Stochastic Differential Equation with Sobolev Coefficients

In this chapter, we will explain how the Brenier’s relaxed variational principle for Euler equation makes involved the ordinary differential equations with Sobolev coefficients and how the
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