Geodesic
Singular integrals and a problem on mixing flows
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 4, pp. 921-943

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We prove a result related to Bressan's mixing problem. We establish an inequality for the change of Bianchini semi-norms of characteristic functions under the flow generated by a divergence free time dependent vector field. The approach leads to a bilinear singular integral operator for which we prove bounds on Hardy spaces. We include additional observations about the approach and a discrete toy version of Bressan's problem.

DOI : 10.1016/j.anihpc.2017.09.001
Classification : 34C11, 35Q35, 37C10, 42B20
Keywords: Mixing flows, Bilinear singular integrals, Bressan's mixing problem, Hardy spaces 
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     title = {Singular integrals and a problem on mixing flows},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Hadžić, Mahir; Seeger, Andreas; Smart, Charles K.; Street, Brian. Singular integrals and a problem on mixing flows. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 4, pp. 921-943. doi: 10.1016/j.anihpc.2017.09.001

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