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EnglishWe introduce the setting of extended metric-topological measure spaces as a general "Wiener like" framework for optimal transport problems and nonsmooth metric analysis in infinite dimension. After a brief review of optimal transport tools for general Radon measures, we discuss the notions of the Cheeger energy, of the Radon measures concentrated on absolutely continuous curves, and of the induced "dynamic transport distances". We study their main properties and their links with the theory of Dirichlet forms and the Bakry-Émery curvature condition, in particular concerning the contractivity properties and the EVI formulation of the induced Heat semigroup.
We introduce the setting of extended metric–topological measure spaces as a general “Wiener like” framework for optimal transport problems and nonsmooth metric analysis in infinite dimension. After a brief review of optimal transport tools for general Radon measures, we discuss the notions of the Cheeger energy, of the Radon measures concentrated on absolutely continuous curves, and of the induced “dynamic transport distances”. We study their main properties and their links with the theory of Dirichlet forms and the Bakry–Emery curvature condition, in particular concerning the contractivity ́ properties and the EVI formulation of the induced Heat semigroup.
| Titolo: | Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces Dedicated to J.L. Vazquez in occasion of his 70th birthday | |
| Autori: | ||
| Data di pubblicazione: | 2016 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.na.2015.12.006 | |
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica | |
| Parole Chiave: | Evolution variational inequality; Heat flow; Optimal transport; | |
| Handle: | http://hdl.handle.net/11384/63360 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| 1-s2.0-S0362546X15004228-main.pdf | Published version | Non pubblico | Administrator Richiedi una copia | |
| Extended_submitted.pdf | Post-Print | Accepted version (post-print) | Non pubblico | Administrator Richiedi una copia |
| 11384_63360.pdf | Submitted version (pre-print) |  | Open Access Visualizza/Apri |
http://hdl.handle.net/11384/63360
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