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On various semiconvex hulls in the calculus of variations

  • Kewei Zhang

Abstract.

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.

Keywords

Distance Function Closed Lamination Polyconvex Hull 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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: kewei@ma.hw.ac.uk GB

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