Abstract
We consider an extended formulation of the transport equation that remains meaningful with discontinuous velocity fields b, assuming that ( 1 , b ) is a special function of bounded deformation (SBD). We study existence, uniqueness, and continuity/stability of the presented formulation. We then apply this study to the problem of fitting to available data a space–time image subject to the optical flow constraint. Moreover, in order to carry out these studies, we refine the SBD approximation theorem of Chambolle to show the convergence of traces.
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