Quasiconvex Hulls in Symmetric Matrices
نویسندگان
چکیده
We analyze the semiconvex hulls of the subset K in symmetric matrices given by K fF M F F jF j a jF j b jF j cg that was rst considered by Dacorogna Tanteri Commun in PDEs We obtain explicit formulae for the polyconvex the quasiconvex and the rank one convex hull for ac b and show in particular that the quasiconvex and the polyconvex hull are di erent if strict inequality holds For ac b we obtain a closed form for the polyconvex and the rank one convex hull
منابع مشابه
F Ur Mathematik in Den Naturwissenschaften Leipzig Quasiconvex Hulls in Symmetric Matrices Quasiconvex Hulls in Symmetric Matrices
We analyze the semiconvex hulls of the subset K in symmetric matrices given by K = fF 2 M 22 : F T = F; jF 11 j = a; jF 12 j = b; jF 22 j = cg that was rst considered by Dacorogna&Tanteri Commun. in PDEs 2001]. We obtain explicit formulae for the polyconvex, the quasiconvex, and the rank-one convex hull for ac ? b 2 0 and show in particular that the quasiconvex and the polyconvex hull are diier...
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