Inventiones mathematicae

, Volume 98, Issue 3, pp 511–547

Ordinary differential equations, transport theory and Sobolev spaces

  • R. J. DiPerna
  • P. L. Lions

DOI: 10.1007/BF01393835

Cite this article as:
DiPerna, R.J. & Lions, P.L. Invent Math (1989) 98: 511. doi:10.1007/BF01393835


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.

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • R. J. DiPerna
    • 1
  • P. L. Lions
    • 2
  1. 1.Department of MathematicsUniversity of BerkeleyBerkeleyUSA
  2. 2.CeremadeUniversité de Paris-DauphineParis Cedex 16France

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