×

Minimizing flows for the Monge-Kantorovich problem. (English) Zbl 1042.49040

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.

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
PDFBibTeX XMLCite
Full Text: DOI