Geodesic
A quantitative theory for the continuity equation
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 7, pp. 1837-1850.

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In this work, we provide stability estimates for the continuity equation with Sobolev vector fields. The results are inferred from contraction estimates for certain logarithmic Kantorovich–Rubinstein distances. As a by-product, we obtain a new proof of uniqueness in the DiPerna–Lions setting. The novelty in the proof lies in the fact that it is not based on the theory of renormalized solutions.

DOI : 10.1016/j.anihpc.2017.01.001
Keywords: Continuity equations, Stability estimates, Logarithmic cost functions, Contraction estimates, Uniqueness 
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Seis, Christian. A quantitative theory for the continuity equation. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 7, pp. 1837-1850. doi : 10.1016/j.anihpc.2017.01.001. http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.01.001/

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