{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:42:44Z","timestamp":1772296964254,"version":"3.50.1"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Interfaces Free Bound."],"published-print":{"date-parts":[[2015,5,26]]},"abstract":"<jats:p>In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions.<\/jats:p>","DOI":"10.4171\/ifb\/333","type":"journal-article","created":{"date-parts":[[2015,5,26]],"date-time":"2015-05-26T17:45:06Z","timestamp":1432662306000},"page":"55-68","source":"Crossref","is-referenced-by-count":23,"title":["Obstacle mean-field game problem"],"prefix":"10.4171","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3129-3956","authenticated-orcid":false,"given":"Diogo A.","family":"Gomes","sequence":"first","affiliation":[{"name":"King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2647-2423","authenticated-orcid":false,"given":"Stefania","family":"Patrizi","sequence":"additional","affiliation":[{"name":"Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany"}]}],"member":"2673","container-title":["Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/IFB\/333","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T12:51:55Z","timestamp":1762951915000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/ifb\/333"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,26]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.4171\/ifb\/333","relation":{},"ISSN":["1463-9963","1463-9971"],"issn-type":[{"value":"1463-9963","type":"print"},{"value":"1463-9971","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,26]]}}}