{"oa":1,"title":"On the geometry of geodesics in discrete optimal transport","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["510"],"intvolume":"        58","date_published":"2019-02-01T00:00:00Z","external_id":{"arxiv":["1805.06040"],"isi":["000452849400001"]},"ec_funded":1,"article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00526-018-1456-1","citation":{"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>","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.","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>.","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>.","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.","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>"},"article_type":"original","quality_controlled":"1","has_accepted_license":"1","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."}],"isi":1,"publisher":"Springer","type":"journal_article","file_date_updated":"2020-07-14T12:47:55Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","day":"01","year":"2019","volume":58,"publication_identifier":{"issn":["09442669"]},"language":[{"iso":"eng"}],"issue":"1","date_created":"2018-12-11T11:44:29Z","date_updated":"2023-09-13T09:12:35Z","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"grant_number":" F06504","_id":"260482E2-B435-11E9-9278-68D0E5697425","name":"Taming Complexity in Partial Di erential Systems","call_identifier":"FWF"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"publication_status":"published","month":"02","file":[{"creator":"dernst","access_level":"open_access","date_created":"2019-01-28T15:37:11Z","date_updated":"2020-07-14T12:47:55Z","file_name":"2018_Calculus_Erbar.pdf","relation":"main_file","file_size":645565,"checksum":"ba05ac2d69de4c58d2cd338b63512798","content_type":"application/pdf","file_id":"5895"}],"scopus_import":"1","oa_version":"Published Version","article_number":"19","_id":"73","status":"public","author":[{"first_name":"Matthias","last_name":"Erbar","full_name":"Erbar, Matthias"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338","first_name":"Jan","last_name":"Maas","full_name":"Maas, Jan"},{"full_name":"Wirth, Melchior","last_name":"Wirth","first_name":"Melchior"}],"publication":"Calculus of Variations and Partial Differential Equations","department":[{"_id":"JaMa"}]}