{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:55:49Z","timestamp":1777449349200,"version":"3.51.4"},"reference-count":27,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T00:00:00Z","timestamp":1462233600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2016,5,3]]},"abstract":"<jats:p>We consider an optimal control problem associated to Dirichlet boundary value problem for linear elliptic equations on a bounded domain \u03a9. We take the matrix-valued coefficients [Formula: see text] of such system as a control in [Formula: see text]. One of the important features of the class of admissible controls is the fact that the matrices [Formula: see text] are unbounded on \u03a9 and eigenvalues of the symmetric parts [Formula: see text] may vanish in \u03a9. In spite of the fact that the equations of this type can exhibit non-uniqueness of weak solutions, the corresponding OCP is well-possed and admits at least one solution. At the same time, optimal solutions to such problem can inherit a singular character of the matrices [Formula: see text]. We indicate two types of optimal solutions to the above problem and show that one of them can not be attained by optimal solutions of regularized problems for coercive elliptic equations with bounded coefficients, using the Steklov smoothing of matrix-valued controls A.<\/jats:p>","DOI":"10.3233\/asy-161365","type":"journal-article","created":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T16:48:24Z","timestamp":1462294104000},"page":"155-188","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["On unbounded optimal controls in coefficients for ill-posed elliptic Dirichlet boundary value problems"],"prefix":"10.1177","volume":"98","author":[{"given":"Thierry","family":"Horsin","sequence":"first","affiliation":[{"name":"Conservatoire National des Arts et M\u00e9tiers, M2N, x IMATH, Case 2D 5000, 292 rue Saint-Martin, 75003 Paris, France. E-mail:\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter I.","family":"Kogut","sequence":"additional","affiliation":[{"name":"Department of Differential Equations, Dnipropetrovsk National University, Gagarin av., 72, 49010 Dnipropetrovsk, Ukraine. E-mail:\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2016,5,3]]},"reference":[{"key":"ref001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2008.07.027"},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1007\/s13163-010-0030-y"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1007\/s000300050004"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02505902"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2032-9_4"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1137\/100815761"},{"key":"ref007","unstructured":"P.\u00a0Drabek, A.\u00a0Kufner and F.\u00a0Nicolosi, Nonlinear Elliptic Equations: Singular and Degenerate Cases, University of West Bohemia, Pilsen, 1996."},{"key":"ref008","unstructured":"L.C.\u00a0Evans and R.F.\u00a0Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992."},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.3934\/mcrf.2015.5.73"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2014.34.2105"},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-011-9840-4"},{"key":"ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8149-4"},{"key":"ref013","doi-asserted-by":"publisher","DOI":"10.4171\/zaa\/1447"},{"key":"ref014","doi-asserted-by":"publisher","DOI":"10.4171\/zaa\/1493"},{"issue":"3","key":"ref015","first-page":"88","volume":"106","author":"Kupenko O.P.","year":"2011","journal-title":"J. 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