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Ordinary differential equations, transport theory and Sobolev spaces

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We 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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References

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Authors and Affiliations

  1. Department of Mathematics, University of Berkeley, 94720, Berkeley, CA, USA

    R. J. DiPerna

  2. Ceremade, Université de Paris-Dauphine, Place de Lattre de Tassigny, F-75775, Paris Cedex 16, France

    P. L. Lions

Authors
  1. R. J. DiPerna
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  2. P. L. Lions
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DiPerna, R.J., Lions, P.L. Ordinary differential equations, transport theory and Sobolev spaces. Invent Math 98, 511–547 (1989). https://doi.org/10.1007/BF01393835

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  • DOI: https://doi.org/10.1007/BF01393835

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