{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:26:39Z","timestamp":1787318799958,"version":"build-2736575974"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We prove necessary conditions for a solution u to the problem of minimizing $\\int_\\Omega[f(\\|\\nabla v(x)\\|)+g(x,v(x))]dx$ in the form of a Pontryagin maximum principle, for f convex and satisfying a growth assumption, but without assuming differentiability.<\/jats:p>","DOI":"10.1137\/080743342","type":"journal-article","created":{"date-parts":[[2009,11,11]],"date-time":"2009-11-11T18:31:07Z","timestamp":1257964267000},"page":"2977-2983","source":"Crossref","is-referenced-by-count":1,"title":["Necessary Conditions for Solutions to Variational Problems"],"prefix":"10.1137","volume":"48","author":[{"given":"A.","family":"Cellina","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Mazzola","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,11,11]]},"reference":[{"key":"R1","unstructured":"R. A. Adams,\n                      Sobolev Spaces\n                      , Academic Press, New York, 1975."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2007.17.449"},{"key":"R3","unstructured":"S. Bianchini and M. Gloyer,\n                      On the Euler-Lagrange equation for a variational problem: The general case\n                      II, Math. Z., to appear."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/060657455"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012996311319"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"F. H. Clarke,\n                      Optimization and Nonsmooth Analysis\n                      , 2nd edition, Classics Appl. Math. 5, SIAM, Philadelphia, 1990.","DOI":"10.1137\/1.9781611971309"},{"key":"R7","unstructured":"L. Pontriagin, V. Boltyianskii, R. Gamkrelidze, and E. Mishchenko,\n                      The Mathematical Theory of Control Processes\n                      , Interscience, New York, 1962."},{"key":"R8","unstructured":"R. T. Rockafellar,\n                      Convex Analysis\n                      , Princeton University Press, Princeton, NJ, 1972."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080743342","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:40:21Z","timestamp":1787316021000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080743342"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,11]]},"references-count":8,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080743342"],"URL":"https:\/\/doi.org\/10.1137\/080743342","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11,11]]}}}