Lipschitz regularity and approximate differentiability of the DiPerna-Lions flow

Luigi Ambrosio, Myriam Lecumberry, and Stefania Maniglia
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Submission date: 04. May. 2005
Pages: 18
published in: Rendiconti del Seminario Matematico della Università di Padova, 114 (2005), p. 29-50 
MSC-Numbers: 35F20, 34A12
Keywords and phrases: $w^{1,p}$ vectorfield, approximate differentiability
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Abstract:
We prove that the flow associated to a vectorfield with a Sobolev regularity p>1, in the space variable is, for any time, approximately differentiable almost everywhere in space.