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In the second case, weaker assumptions of measurability type are shown to be sufficient for the existence of the optimal material distribution. We impose no restriction on the dimension of the underlying Euclidean space.<\/jats:p>","DOI":"10.1137\/s0363012901388142","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1440-1454","source":"Crossref","is-referenced-by-count":10,"title":["Existence for Shape Optimization Problems in Arbitrary Dimension"],"prefix":"10.1137","volume":"41","author":[{"given":"W. B.","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Neittaanm\u00e4ki","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D.","family":"Tiba","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","volume-title":"Sobolev spaces","author":"Adams Robert","year":"1975"},{"key":"R2","volume-title":"Analyse fonctionnelle","author":"Brezis Ha\u00efm","year":"1983"},{"key":"R3","first-page":"57","volume":"319","author":"Bucur Dorin","year":"1994","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"key":"R4","first-page":"795","volume":"318","author":"Bucur Dorin","year":"1994","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. 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