Liero, M. and Mielke, A. and Savaré, G. (2016) Optimal Transport in Competition with Reaction: The HellingerKantorovich Distance and Geodesic Curves. SIAM J. Math. Anal., 48 (2). pp. 28692911. ISSN 10957154 (online)

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Official URL: http://dx.doi.org/10.1137/15M1041420
Abstract
We discuss a new notion of distance on the space of finite and nonnegative measures on $\Omega \subset {\mathbb R}^d$, which we call the HellingerKantorovich distance. It can be seen as an infconvolution of the wellknown KantorovichWasserstein distance and the HellingerKakutani distance. The new distance is based on a dynamical formulation given by an Onsager operator that is the sum of a Wasserstein diffusion part and an additional reaction part describing the generation and absorption of mass. We present a full characterization of the distance and some of its properties. In particular, the distance can be equivalently described by an optimal transport problem on the cone space over the underlying space $\Omega$. We give a construction of geodesic curves and discuss examples and their general properties.
Item Type:  Article 

Additional Information:  SFB 1114 Preprint 09/2015 in arXiv:1508.00068 
Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
ID Code:  2181 
Deposited By:  Silvia Hoemke 
Deposited On:  16 Jan 2018 17:00 
Last Modified:  16 Jan 2018 17:00 
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