Preprint 47/2001

Quasiconvex hulls in symmetric matrices

Georg Dolzmann

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Submission date: 05. Aug. 2001
Pages: 14
MSC-Numbers: 74N15, 49M20
Keywords and phrases: polyconvexity, quasiconvexity, rank-1 convexity, semiconvex hulls
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We analyze the semiconvex hulls of the subset K in symmetric matrices given by tex2html_wrap_inline16 that was first considered by Dacorogna & Tanteri [Commun. in PDEs 2001]. We obtain explicit formulae for the polyconvex, the quasiconvex, and the rank-one convex hull for tex2html_wrap_inline18 and show in particular that the quasiconvex and the polyconvex hull are different if strict inequality holds. For tex2html_wrap_inline20 we obtain a closed form for the polyconvex and the rank-one convex hull.

24.11.2021, 02:11