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Publications (3)1 Total impact

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    ABSTRACT: If ›j 2R d are bounded open subsets and ' 2 C 1 (›1 ; ›2) respects Lebesgue measure and satisfles F - ' 2 BV (›1) for all F 2 BV (›2) then ' is uniformly Lipshitzean. The problem addressed in this note was motivated by the study of the propagation of regularity in the transport by vector flelds with bounded divergence, @u @t + d X j=1 aj(x;t) @u @xj = 0; x 2 R
    Methods and Applications of Analysis. 01/2011; 18(2).
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    ABSTRACT: We give examples of divergence free vector fields. For such fields the Cauchy problem for the linear transport equation has unique bounded solutions. The first example has nonuniqueness in the Cauchy problem for the ordinary differential equation defining characteristics. In addition, there are smooth initial data so that the unique bounded solution is not continuous on any neighborhood of the origin. The second example is a field of similar regularity and intial data of bounded variation.
    Communications in mathematical sciences 01/2004; · 1.00 Impact Factor
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    ABSTRACT: We present an example of a uniformly bounded divergence free vector eld a(x):@x on R3 which has the property that the linear transport equation @u @t + d X i=1 aj(t; x) @u @xj = 0 ; div a = d X i=1 @aj @xj = 0 (1) has a nontrivial bounded solution with vanishing Cauchy data. The coecien ts have the property that x3ra is a bounded measure. For the same equation we prove uniqueness in the Cauchy problem when the coecien ts a and u belong to (H 1=2 \ L1)((0; T ) Rd).
    Séminaire Équations aux Dérivées Partielles. 01/2003;