Ordinary differential equations, transport theory and Sobolev spaces

@article{Diperna1989OrdinaryDE,
  title={Ordinary differential equations, transport theory and Sobolev spaces},
  author={Ronald J. Diperna and Pierre-Louis Lions},
  journal={Inventiones mathematicae},
  year={1989},
  volume={98},
  pages={511-547}
}
SummaryWe obtain some new existence, uniqueness and stability results for ordinary differential equations with coefficients in Sobolev spaces. These results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions. 

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