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Under a density condition we show existence of Lagrange multipliers, which have a representation via measures and additional regularity properties.<\/jats:p>","DOI":"10.1137\/080727610","type":"journal-article","created":{"date-parts":[[2009,7,18]],"date-time":"2009-07-18T04:19:08Z","timestamp":1247890748000},"page":"2407-2432","source":"Crossref","is-referenced-by-count":6,"title":["State Constrained Optimal Control Problems with States of Low Regularity"],"prefix":"10.1137","volume":"48","author":[{"given":"Anton","family":"Schiela","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,7,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1080\/01630569708816758"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"H. Amann,\n                      Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems\n                      , in Function Spaces, Differential Operators and Nonlinear Analysis, H. J. Schmeisser and H. Triebel, eds., Teubner, Stuttgart, Leipzig, 1993, pp. 9\u2013126.","DOI":"10.1007\/978-3-663-11336-2_1"},{"key":"R3","unstructured":"R. B. Ash,\n                      Measure, Integration and Functional Analysis\n                      , Academic Press, New York, 1972."},{"key":"R4","unstructured":"J. M. Borwein and Q. J. Zhu,\n                      Techniques of Variational Analysis\n                      , CMS Books Math. Ouvrages Math. SMC, Springer, New York, 2005."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0324078"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/0331044"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012995283637"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01182597"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"I. Ekeland and R. T\u00e9mam,\n                      Convex Analysis and Variational Problems\n                      , Classics Appl. Math. 28, SIAM, Philadelphia, 1999.","DOI":"10.1137\/1.9781611971088"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"D. H. Fremlin,\n                      Toplogical Riesz Spaces and Measure Theory\n                      , Cambridge University Press, New York, 1974.","DOI":"10.1017\/CBO9780511897207"},{"key":"R11","unstructured":"S. Goldberg,\n                      Unbounded Linear Operators\n                      , Dover, New York, 1966."},{"key":"R12","unstructured":"R. Haller-Dintelmann, C. Meyer, J. Rehberg, and A. Schiela,\n                      H\u00f6lder continuity and optimal control for nonsmooth elliptic problems\n                      , Appl. Math. Optim., to appear."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/050637480"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.08.008"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-005-3056-1"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1.2.130"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"R. T. Rockafellar,\n                      Conjugate Duality and Optimization\n                      , CBMS-NSF Regional Conf. Ser. in Appl. Math. 16, SIAM, Philadelphia, 1974.","DOI":"10.1137\/1.9781611970524"},{"key":"R18","unstructured":"A. Schiela,\n                      Barrier methods for optimal control problems with state constraints\n                      , SIAM J. 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Werner,\n                      Funktionalanalysis\n                      , 3rd ed., Springer, Berlin, 2000."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1007\/BF01442543"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080727610","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:51:38Z","timestamp":1787316698000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080727610"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/080727610"],"URL":"https:\/\/doi.org\/10.1137\/080727610","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}