{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:32:48Z","timestamp":1777447968711,"version":"3.51.4"},"reference-count":26,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T00:00:00Z","timestamp":1562889600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2019,7,12]]},"abstract":"<jats:p>We establish two types of characterizations for high order anisotropic Sobolev spaces. In particular, we prove high order anisotropic versions of Bourgain\u2013Brezis\u2013Mironescu\u2019s formula and Nguyen\u2019s formula.<\/jats:p>","DOI":"10.3233\/asy-181515","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T13:58:49Z","timestamp":1562939929000},"page":"239-260","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Characterizations of anisotropic high order Sobolev spaces"],"prefix":"10.1177","volume":"113","author":[{"given":"Nguyen","family":"Lam","sequence":"first","affiliation":[{"name":"Department of Mathematics and The Pacific Institute for the Mathematical Sciences, University of British Columbia, Vancouver, BC V6T1Z4, Canada. 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E-mail:\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,7,12]]},"reference":[{"key":"ref001","doi-asserted-by":"publisher","DOI":"10.1007\/s00229-010-0399-4"},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1142\/S0219199711004439"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-15239"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.3233\/ASY-2007-810"},{"key":"ref005","unstructured":"J.\u00a0Bourgain, H.\u00a0Brezis and P.\u00a0Mironescu, Another look at Sobolev spaces, in: Optimal Control and Partial Differential Equations. A Volume in Honor of Professor Alain Bensoussan\u2019s 60th Birthday, J.L.\u00a0Menaldi, E.\u00a0Rofman and A.\u00a0Sulem, eds, IOS Press, Amsterdam, 2001, pp.\u00a0439\u2013455."},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02868470"},{"key":"ref007","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2006.05.021"},{"key":"ref008","doi-asserted-by":"publisher","DOI":"10.1070\/RM2002v057n04ABEH000533"},{"key":"ref009","first-page":"223","volume":"26","author":"Brezis H.","year":"2015","journal-title":"Rend Accad. Lincei"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2016.02.005"},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2014.08.004"},{"key":"ref012","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2015.01.003"},{"key":"ref013","unstructured":"S.\u00a0Di Marino and M.\u00a0Squassina, New characterizations of Sobolev metric spaces, 2018, preprint. Available at: http:\/\/cvgmt.sns.it\/paper\/3791\/."},{"key":"ref014","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2019.06.014"},{"key":"ref015","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/181"},{"key":"ref016","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2018.08.005"},{"key":"ref017","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2006.04.001"},{"key":"ref018","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-010-0373-8"},{"key":"ref019","doi-asserted-by":"publisher","DOI":"10.1515\/anona-2017-0239"},{"key":"ref020","doi-asserted-by":"publisher","DOI":"10.1080\/17476933.2018.1520850"},{"key":"ref021","unstructured":"H.M.\u00a0Nguyen and M.\u00a0Squassina, On anisotropic Sobolev spaces,\n                      Commun. Contemp. 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