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Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of the pressure in the deformed configuration. We also provide a convex relaxation of the problem together with its dual formulation, based on measure valued mappings, which coincides with the original problem under our condition.<\/jats:p>","DOI":"10.1137\/20m1333377","type":"journal-article","created":{"date-parts":[[2021,2,16]],"date-time":"2021-02-16T11:27:40Z","timestamp":1613474860000},"page":"1070-1087","source":"Crossref","is-referenced-by-count":2,"title":["Hidden Convexity in a Problem of Nonlinear Elasticity"],"prefix":"10.1137","volume":"53","author":[{"given":"Nassif","family":"Ghoussoub","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6920-603X","authenticated-orcid":true,"given":"Young-Heon","family":"Kim","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2597-1124","authenticated-orcid":true,"given":"Hugo","family":"Lavenant","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2731-6895","authenticated-orcid":true,"given":"Aaron Zeff","family":"Palmer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,2,16]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-014-0754-9"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00279992"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-21791-6_1"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-0174-2_1"},{"key":"atypb5","first-page":"805","volume":"305","author":"Brenier Y.","year":"1987","journal-title":"C. 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Louet,\n                      Optimal Transport Problems with Gradient Penalization\n                      , PhD thesis, Universit\u00e9 Paris Sud, 2014."},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2019.01137"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500029929"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-20828-2"},{"key":"atypb28","first-page":"115","volume":"487","author":"Urbas J.","year":"1997","journal-title":"J. Reine Angew. 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