{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:36:52Z","timestamp":1787319412990,"version":"build-2736575974"},"reference-count":15,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>The minimum time function $T(\\cdot)$ of smooth control systems is known to be locally semiconcave provided Petrov's controllability condition is satisfied. Moreover, such a regularity holds up to the boundary of the target under an inner ball assumption. We generalize this analysis to differential inclusions, replacing the above hypotheses with the continuity of $T(\\cdot)$ near the target, and an inner ball property for the multifunction associated with the dynamics. In such a weakened setup, we prove that the hypograph of $T(\\cdot)$ satisfies, locally, an exterior sphere condition. As is well known, this geometric property ensures most of the regularity results that hold for semiconcave functions, without assuming $T(\\cdot)$ to be Lipschitz.<\/jats:p>","DOI":"10.1137\/110825078","type":"journal-article","created":{"date-parts":[[2011,12,13]],"date-time":"2011-12-13T18:27:16Z","timestamp":1323800836000},"page":"2558-2576","source":"Crossref","is-referenced-by-count":11,"title":["Exterior Sphere Condition and Time Optimal Control for Differential Inclusions"],"prefix":"10.1137","volume":"49","author":[{"given":"Piermarco","family":"Cannarsa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Khai T.","family":"Nguyen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,12,13]]},"reference":[{"key":"R1","unstructured":"J.P. Aubin and H. Frankowska,\n                      Set-Valued Analysis\n                      , Birkh\u00e4user, Boston, 1990."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(88)90132-5"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0329068"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2006002"},{"key":"R5","unstructured":"P. Cannarsa, F. Marino, and P. R. Wolenski,\n                      Semiconcavity of the minimum time function for differential inclusions\n                      , Dyn. Contin. Discrete Impuls. Syst. Ser. B, to appear."},{"key":"R6","doi-asserted-by":"crossref","unstructured":"P. Cannarsa and C. Sinestrari,\n                      Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control\n                      , Birkh\u00e4user, Boston, 2004.","DOI":"10.1007\/b138356"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01189393"},{"key":"R8","doi-asserted-by":"crossref","first-page":"453","DOI":"10.3934\/dcds.2011.29.453","volume":"29","author":"Cannarsa P.","year":"2011","journal-title":"Discrete Contin. Dyn. Syst.","ISSN":"https:\/\/id.crossref.org\/issn\/1078-0947","issn-type":"print"},{"key":"R9","unstructured":"F. H. Clarke,\n                      Optimization and Nonsmooth Analysis\n                      , Canad. Math. Soc. Ser. Monogr. Adv. Texts, John Wiley & Sons, New York, 1983."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-005-0352-7"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/090774549"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2010.07.010"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2010.04.001"},{"key":"R14","first-page":"33","volume":"83","author":"Ornelas A.","year":"1990","journal-title":"Rend. Sem. Mat. Univ. Padova","ISSN":"https:\/\/id.crossref.org\/issn\/0041-8994","issn-type":"print"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012996299338"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/110825078","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:48:35Z","timestamp":1787316515000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/110825078"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":15,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1137\/110825078"],"URL":"https:\/\/doi.org\/10.1137\/110825078","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1]]}}}