Angenent, Sigurd; Haker, Steven; Tannenbaum, Allen Minimizing flows for the Monge-Kantorovich problem. (English) Zbl 1042.49040 SIAM J. Math. Anal. 35, No. 1, 61-97 (2003). Summary: We formulate a new minimizing flow for the optimal mass transport (Monge-Kantorovich) problem. We study certain properties of the flow, including weak solutions as well as short- and long-term existence. Optimal transport has found a number of applications, including econometrics, fluid dynamics, cosmology, image processing, automatic control, transportation, statistical physics, shape optimization, expert systems, and meteorology. Cited in 3 ReviewsCited in 37 Documents MSC: 49Q20 Variational problems in a geometric measure-theoretic setting 49J45 Methods involving semicontinuity and convergence; relaxation 94A08 Image processing (compression, reconstruction, etc.) in information and communication theory 92C55 Biomedical imaging and signal processing Keywords:optimal transport; gradient flows; weak solutions; image registration; medical imaging PDFBibTeX XMLCite \textit{S. Angenent} et al., SIAM J. Math. Anal. 35, No. 1, 61--97 (2003; Zbl 1042.49040) Full Text: DOI