Uniqueness of continuous solutions for BV vector fields

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Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients (2008, background): “…having proved this, in [1] the well-posedness of the continuity equations in L∞ is proved in the case of vector fields with BV regularity whose distributional divergence belongs to L∞ (for other similar results on the well-posedness of the transport/continuity equation, see also [6, 7, 13, 11]).”
Differential equations with singular fields (2010, background): “This last assumption b ∈ BV was also considered in [15] and [16].”
Transport equation and Cauchy problem for BV vector fields (2004, background): “This idea is further developed by F. Colombini and N. Lerner in [19], where they define a class of “conormal BV vector fields”, invariant under bi-Lipschitz transformations and including the class considered in [31] (see also [ 18 ] for uniqueness results for continuous solutions) and prove a unique”
Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients (2005, background): “g [13], [7], [8] and the references therein).”
Trace theorems and spatial continuity properties for the solutions of the transport equation (2005, background): “The uniqueness of solutions in the class L∞(]0, T [, C0 b (R)) for vector fields in L(1)(]0, T [, (BVloc(R))) with bounded divergence and suitable behavior at infinity is proved in [6].”