Absolutely continuous and BV-curves in 1-Wasserstein spaces

DOI10.1007/S00526-023-02616-1zbMath1529.60014arXiv2209.04268OpenAlexW4389323846MaRDI QIDQ6140835

Timo Schultz, Zhenhao Li, Ehsan Abedi

Publication date: 2 January 2024

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.04268

zbMATH Keywords

superposition principleabsolutely continuous curves1-Wasserstein spaceBV-curvescharacterization of geodesics

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Existence theories for problems in abstract spaces (49J27) Functions of bounded variation, generalizations (26A45) Existence of optimal solutions to problems involving randomness (49J55) Optimal transportation (49Q22)

Cites Work

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• Gradient flows of the entropy for finite Markov chains
• Lazy random walks and optimal transport on graphs
• Characterization of absolutely continuous curves in Wasserstein spaces
• Ricci curvature of finite Markov chains via convexity of the entropy
• Ricci curvature for metric-measure spaces via optimal transport
• Absolutely continuous curves in extended Wasserstein−Orlicz spaces

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