{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T21:33:44Z","timestamp":1780436024763,"version":"3.54.1"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2012,10,1]],"date-time":"2012-10-01T00:00:00Z","timestamp":1349049600000},"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":[[2012,10]]},"abstract":"<jats:p>In this paper, we study the Dirichlet problem for an elliptic equation, in which the 1-Laplacian operator and lower-order terms appear. We introduce a suitable definition of solution and prove the existence of, at least, one bounded solution in BV(\u03a9) having a negligible jump part. Moreover, a uniqueness result for small positive data is proved, and explicit examples of solutions are shown.<\/jats:p>","DOI":"10.3233\/asy-2012-1099","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:23:18Z","timestamp":1575055398000},"page":"21-43","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":11,"title":["Bounded solutions to the 1-Laplacian equation with a critical gradient term"],"prefix":"10.1177","volume":"80","author":[{"given":"Fuensanta","family":"Andreu","sequence":"first","affiliation":[{"name":"Departament d'An\u00e0lisi Matem\u00e0tica, Universitat de Val\u00e8ncia, Burjassot, Valencia, Spain. E-mail: sergio.segura@uv.es"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrea","family":"Dall'Aglio","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Roma \u201cLa Sapienza\u201d, Roma, Italy. E-mail: dallaglio@mat.uniroma1.it"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sergio","family":"Segura de Le\u00f3n","sequence":"additional","affiliation":[{"name":"Departament d'An\u00e0lisi Matem\u00e0tica, Universitat de Val\u00e8ncia, Burjassot, Valencia, Spain. E-mail: sergio.segura@uv.es"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2012,10,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2012-1099","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2012-1099","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:42Z","timestamp":1777379982000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2012-1099"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,10]]}},"alternative-id":["10.3233\/ASY-2012-1099"],"URL":"https:\/\/doi.org\/10.3233\/asy-2012-1099","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10]]}}}