{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:26:37Z","timestamp":1787318797741,"version":"build-2736575974"},"reference-count":33,"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>The present paper is dedicated to the verification of sufficient second order conditions for shape optimization problems that arise from stationary free boundary problems. We assume that the state satisfies the Dirichlet problem for the Poisson equation and track the Neumann data at the free boundary. The gradient and Hessian of the shape functional under consideration are computed. By analyzing the shape Hessian in case of matching data a sufficient criterion for its strict coercivity is derived. Strict coercivity implies stable minimizers and, in case of a Ritz\u2013Galerkin method, existence and convergence of approximate shapes. By a fast boundary element method we realize an efficient numerical algorithm to solve the free boundary problem. Numerical experiments are carried out in three spatial dimensions.<\/jats:p>","DOI":"10.1137\/080733760","type":"journal-article","created":{"date-parts":[[2009,11,5]],"date-time":"2009-11-05T18:18:20Z","timestamp":1257445100000},"page":"2901-2916","source":"Crossref","is-referenced-by-count":18,"title":["Tracking Neumann Data for Stationary Free Boundary Problems"],"prefix":"10.1137","volume":"48","author":[{"given":"Karsten","family":"Eppler","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Helmut","family":"Harbrecht","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,11,5]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1002\/mma.1670100102"},{"key":"R2","first-page":"105","volume":"325","author":"Alt H. W.","year":"1981","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"key":"R3","unstructured":"D. Colton and R. Kress,\n                      Integral Equation Methods in Scattering Theory\n                      , in Pure Appl. Math. (N.Y.), Wiley, Chichester, 1983."},{"key":"R4","first-page":"95","volume":"96","author":"Dambrine M.","year":"2002","journal-title":"RACSAM, Rev. R. Acad. Cienc. Ser. A Mat."},{"key":"R5","unstructured":"M. C. Delfour and J. P. Zolesio,\n                      Shapes and Geometries: Analysis, Differential Calculus, and Optimization\n                      , Adv. Des. Control 4, SIAM, Philadelphia, 2001."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903428852"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385864"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-99-01092-3"},{"key":"R9","unstructured":"J. E. Dennis and R. B. Schnabel,\n                      Numerical Methods for Nonlinear Equations and Unconstrained Optimization Techniques\n                      , Prentice\u2013Hall, Englewood Cliffs, NJ, 1983."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.7151\/dmdico.1005"},{"key":"R11","first-page":"487","volume":"10","author":"Eppler K.","year":"2000","journal-title":"J. Appl. Math. Comput. Sci."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2006.03.017"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/j.enganabound.2007.10.020"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-007-9076-2"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/05062679X"},{"key":"R16","first-page":"165","volume":"486","author":"Flucher M.","year":"1997","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(87)90140-9"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"C. Grossmann and J. Terno,\n                      Numerik der Optimierung\n                      , Teubner, Stuttgart, 1993.","DOI":"10.1007\/978-3-322-93110-8"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1007\/PL00021408"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1002\/mana.200310171"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827503429387"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026095405906"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.4171\/ifb\/213"},{"key":"R24","doi-asserted-by":"crossref","unstructured":"F. Murat and J. Simon,\n                      \u00c9tude de probl\u00e8mes d'optimal design\n                      , in Optimization Techniques, Modeling and Optimization in the Service of Man, Lecture Notes in Comput. Sci. 41, J. C\u00e9a, ed., Springer, Berlin, 1976, pp. 54\u201362.","DOI":"10.1007\/3-540-07623-9_279"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994272957"},{"key":"R26","doi-asserted-by":"crossref","unstructured":"T. von Petersdorff and C. Schwab,\n                      Fully discretized multiscale Galerkin BEM\n                      , in Multiscale Wavelet Methods for PDEs, W. Dahmen, A. Kurdila, and P. Oswald, eds., Academic Press, San Diego, 1997, pp. 287\u2013346.","DOI":"10.1016\/S1874-608X(97)80009-X"},{"key":"R27","doi-asserted-by":"crossref","unstructured":"O. Pironneau,\n                      Optimal Shape Design for Elliptic Systems\n                      , Springer, New York, 1983.","DOI":"10.1007\/978-3-642-87722-3"},{"key":"R28","doi-asserted-by":"crossref","unstructured":"R. Schneider,\n                      Multiskalen- und Wavelet-Matrixkompression: Analysisbasierte Methoden zur L\u00f6sung gro\u00dfer vollbesetzter Gleichungssyteme\n                      , Teubner, Stuttgart, 1998.","DOI":"10.1007\/978-3-663-10851-1"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.1980.10120631"},{"key":"R30","doi-asserted-by":"crossref","unstructured":"J. Sokolowski and J.P. Zolesio,\n                      Introduction to Shape Optimization\n                      , Springer, Berlin, 1992.","DOI":"10.1007\/978-3-642-58106-9"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1137\/0506045"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1997310708051"},{"key":"R33","doi-asserted-by":"crossref","unstructured":"J. Wloka,\n                      Partial Differential Equations\n                      , Cambridge University Press, Cambridge, 1987.","DOI":"10.1017\/CBO9781139171755"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080733760","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:40:10Z","timestamp":1787316010000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080733760"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,5]]},"references-count":33,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080733760"],"URL":"https:\/\/doi.org\/10.1137\/080733760","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11,5]]}}}