[{"publication_status":"published","title":"On the geometry of geodesics in discrete optimal transport","oa":1,"article_type":"original","_id":"73","month":"02","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"JaMa"}],"status":"public","article_number":"19","abstract":[{"lang":"eng","text":"We consider the space of probability measures on a discrete set X, endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset Y⊆X, it is natural to ask whether they can be connected by a constant speed geodesic with support in Y at all times. Our main result answers this question affirmatively, under a suitable geometric condition on Y introduced in this paper. The proof relies on an extension result for subsolutions to discrete Hamilton-Jacobi equations, which is of independent interest."}],"ec_funded":1,"intvolume":"        58","citation":{"ama":"Erbar M, Maas J, Wirth M. On the geometry of geodesics in discrete optimal transport. <i>Calculus of Variations and Partial Differential Equations</i>. 2019;58(1). doi:<a href=\"https://doi.org/10.1007/s00526-018-1456-1\">10.1007/s00526-018-1456-1</a>","short":"M. Erbar, J. Maas, M. Wirth, Calculus of Variations and Partial Differential Equations 58 (2019).","mla":"Erbar, Matthias, et al. “On the Geometry of Geodesics in Discrete Optimal Transport.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 58, no. 1, 19, Springer, 2019, doi:<a href=\"https://doi.org/10.1007/s00526-018-1456-1\">10.1007/s00526-018-1456-1</a>.","ieee":"M. Erbar, J. Maas, and M. Wirth, “On the geometry of geodesics in discrete optimal transport,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 58, no. 1. Springer, 2019.","ista":"Erbar M, Maas J, Wirth M. 2019. On the geometry of geodesics in discrete optimal transport. Calculus of Variations and Partial Differential Equations. 58(1), 19.","apa":"Erbar, M., Maas, J., &#38; Wirth, M. (2019). On the geometry of geodesics in discrete optimal transport. <i>Calculus of Variations and Partial Differential Equations</i>. Springer. <a href=\"https://doi.org/10.1007/s00526-018-1456-1\">https://doi.org/10.1007/s00526-018-1456-1</a>","chicago":"Erbar, Matthias, Jan Maas, and Melchior Wirth. “On the Geometry of Geodesics in Discrete Optimal Transport.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00526-018-1456-1\">https://doi.org/10.1007/s00526-018-1456-1</a>."},"day":"01","has_accepted_license":"1","language":[{"iso":"eng"}],"arxiv":1,"type":"journal_article","file_date_updated":"2020-07-14T12:47:55Z","doi":"10.1007/s00526-018-1456-1","publisher":"Springer","issue":"1","publication":"Calculus of Variations and Partial Differential Equations","author":[{"first_name":"Matthias","full_name":"Erbar, Matthias","last_name":"Erbar"},{"orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","full_name":"Maas, Jan","last_name":"Maas"},{"last_name":"Wirth","first_name":"Melchior","full_name":"Wirth, Melchior"}],"ddc":["510"],"external_id":{"isi":["000452849400001"],"arxiv":["1805.06040"]},"oa_version":"Published Version","date_published":"2019-02-01T00:00:00Z","file":[{"relation":"main_file","checksum":"ba05ac2d69de4c58d2cd338b63512798","file_size":645565,"creator":"dernst","file_name":"2018_Calculus_Erbar.pdf","content_type":"application/pdf","file_id":"5895","date_created":"2019-01-28T15:37:11Z","access_level":"open_access","date_updated":"2020-07-14T12:47:55Z"}],"isi":1,"volume":58,"year":"2019","date_created":"2018-12-11T11:44:29Z","quality_controlled":"1","project":[{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425","grant_number":" F06504","name":"Taming Complexity in Partial Di erential Systems"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"date_updated":"2023-09-13T09:12:35Z","publication_identifier":{"issn":["09442669"]},"scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)"}]