On various semiconvex hulls in the calculus of variations

  • Kewei Zhang


We show that for any compact set \(K\subset M^{N\times n}\), \(L_c(K)=C(K)\) if and only if \(Q(K)=C(K)\), \(L_c(K)\), \(Q(K)\) and \(C(K)\) being the closed lamination convex hull, quasiconvex hull and convex hull of \(K\) respectively. When \(K\subset M^{2\times 2}\), we show that \(L_c(K)=C(K)\) if and only if \(P(K)=C(K)\), where \(P(K)\) is the polyconvex hull of \(K\). We give some estimates of these relations by using quasiconvexifications of distance functions.


Distance Function Closed Lamination Polyconvex Hull 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Kewei Zhang
    • 1
  1. 1. Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS UK; E-mail address: GB

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