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