{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:40:56Z","timestamp":1787323256557,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2002,1]]},"abstract":"<jats:p>\n                    We consider the problem of minimizing autonomous, simple integrals such as \\min\\,\\left\\{ \\int_0^T f\\left(x(t)\\,,x^\\prime(t)\\right)\\,dt\\colon\\,\\, \\text{$x\\in AC{([0\\,,T])}$, $x(0)=x_0$, $x(T)=x_T$} \\right\\}, \\tag{$\\cal{P}$} where $f:{\\mathbb R}\\times{\\mathbb R} \\to [0,\\infty]$ is a possibly nonconvex function with either superlinear or slow growth at infinity. Assuming that the relaxed problem ($\\cal{P}^{\\ast\\ast}$)---obtained from ($\\cal{P}$) by replacing f with its convex envelope f\n                    <jats:sup>**<\/jats:sup>\n                    with respect to the derivative variable $x^\\prime$---admits a solution, we prove attainment for ($\\cal{P}$) under mild regularity and growth assumptions on f and f\n                    <jats:sup>**<\/jats:sup>\n                    . We discuss various instances of growth conditions on f that yield solutions to the corresponding relaxed problem ($\\cal{P}^{\\ast\\ast}$), and we present examples that show that the hypotheses on f and f\n                    <jats:sup>**<\/jats:sup>\n                    considered here for attainment are essentially sharp.\n                  <\/jats:p>","DOI":"10.1137\/s0363012901387999","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1118-1140","source":"Crossref","is-referenced-by-count":7,"title":["Existence of Minimizers for Nonconvex, Noncoercive Simple Integrals"],"prefix":"10.1137","volume":"41","author":[{"given":"P.","family":"Celada","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Perrotta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(79)90075-5"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.2000.3839"},{"key":"R3","unstructured":"A. Cellina,\n                      The classical problem of the Calculus of Variations in the autonomous case: Relaxation and Lipschitzianity of solutions\n                      , preprint, Universit\u00e1 degli Studi di Milano Bicocca, Italy, 2001."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/s0294-1449(16)30306-7"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1994-1174488-2"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1996.0069"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1993-1118823-3"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(95)00010-S"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012994278201"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0327-8"},{"key":"R11","unstructured":"I. Ekeland and R. Temam,\n                      Convex Analysis and Variational Problems\n                      , Stud. Math. Appl. 1, North Holland, Amsterdam, 1976."},{"key":"R12","first-page":"167","volume":"55","author":"Fusco N.","year":"1998","journal-title":"Portugal. Math."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01765844"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"Paolo Marcellini, Nonconvex integrals of the calculus of variations, Lecture Notes in Math., Vol. 1446, Springer, Berlin, 1990, 16\u20135791j:49002","DOI":"10.1007\/BFb0084930"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1993.1188"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02192088"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1998.5915"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(87)90164-1"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/s0294-1449(16)30371-7"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1007\/BF02192219"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0363012901387999","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:51:21Z","timestamp":1787320281000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0363012901387999"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2002,1]]}},"alternative-id":["10.1137\/S0363012901387999"],"URL":"https:\/\/doi.org\/10.1137\/s0363012901387999","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,1]]}}}