{"created":"2023-06-26T11:01:14.238822+00:00","id":1901,"links":{},"metadata":{"_buckets":{"deposit":"fb95942a-b648-42e6-8750-ce78ce13b8e9"},"_deposit":{"created_by":28,"id":"1901","owners":[28],"pid":{"revision_id":0,"type":"depid","value":"1901"},"status":"published"},"_oai":{"id":"oai:oist.repo.nii.ac.jp:00001901","sets":["6:212"]},"author_link":["12580","12579","12578"],"item_10001_biblio_info_7":{"attribute_name":"Bibliographic Information","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2020-10-21","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"1014","bibliographicPageStart":"979","bibliographicVolumeNumber":"272","bibliographic_titles":[{},{"bibliographic_title":"Journal of Differential Equations","bibliographic_titleLang":"en"}]}]},"item_10001_creator_3":{"attribute_name":"Author","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Liu, Qing"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Shanmugalingam, Nageswari"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Zhou, Xiaodan"}],"nameIdentifiers":[{}]}]},"item_10001_description_5":{"attribute_name":"Abstract","attribute_value_mlt":[{"subitem_description":"In this paper we prove the equivalence between some known notions of solutions to the eikonal equation and more general analogs of the Hamilton-Jacobi equations in complete and rectifiably connected metric spaces. The notions considered are that of curve-based viscosity solutions, slope-based viscosity solutions, and Monge solutions. By using the induced intrinsic (path) metric, we reduce the metric space to a length space and show the equivalence of these solutions to the associated Dirichlet boundary problem. Without utilizing the boundary data, we also localize our argument and directly prove the equivalence for the definitions of solutions. Regularity of solutions related to the Euclidean semi-concavity is discussed as well.","subitem_description_type":"Other"}]},"item_10001_publisher_8":{"attribute_name":"Publisher","attribute_value_mlt":[{"subitem_publisher":"Elsevier"}]},"item_10001_relation_14":{"attribute_name":"DOI","attribute_value_mlt":[{"subitem_relation_type":"isVersionOf","subitem_relation_type_id":{"subitem_relation_type_id_text":"info:doi/10.1016/j.jde.2020.10.018","subitem_relation_type_select":"DOI"}}]},"item_10001_relation_17":{"attribute_name":"Related site","attribute_value_mlt":[{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://www.sciencedirect.com/science/article/pii/S002203962030560X","subitem_relation_type_select":"URI"}}]},"item_10001_rights_15":{"attribute_name":"Rights","attribute_value_mlt":[{"subitem_rights":"This article/chapter was published in Journal of Differential Equations, Volume 272, Qing Liu, Nageswari Shanmugalingam, Xiaodan Zhou, Equivalence of solutions of eikonal equation in metric spaces, Page 979-1014, © Elsevier 2020."}]},"item_10001_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"0022-0396","subitem_source_identifier_type":"ISSN"}]},"item_10001_version_type_20":{"attribute_name":"Author's flag","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2022-10-21"}],"displaytype":"detail","filename":"HJ_metric_final.pdf","filesize":[{"value":"554.1 kB"}],"format":"application/pdf","license_note":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International(https://creativecommons.org/licenses/by-nc-nd/4.0/)","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"HJ_metric_final","url":"https://oist.repo.nii.ac.jp/record/1901/files/HJ_metric_final.pdf"},"version_id":"405b0ab9-f4c2-4d98-87d7-10b2b7862698"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Eikonal equation","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"Viscosity solutions","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"Metric spaces","subitem_subject_language":"en","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"journal article","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Equivalence of solutions of eikonal equation in metric spaces","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Equivalence of solutions of eikonal equation in metric spaces","subitem_title_language":"en"}]},"item_type_id":"10001","owner":"28","path":["212"],"pubdate":{"attribute_name":"公開日","attribute_value":"2021-01-20"},"publish_date":"2021-01-20","publish_status":"0","recid":"1901","relation_version_is_last":true,"title":["Equivalence of solutions of eikonal equation in metric spaces"],"weko_creator_id":"28","weko_shared_id":28},"updated":"2023-06-26T11:40:39.351761+00:00"}