Geodesic
Estimates of Quasiconvex Polytopes in the Calculus of Variations
Journal of convex analysis, Tome 13 (2006) no. 1, pp. 37-5

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\def\dist{\operatorname{dist}} We give direct estimates for the quasiconvex polytopes $Q(K)$ generated by a finite set $K\subset M^{N\times n}$. More precisely, we bound the quasiconvex envelope $Q\dist(\cdot,K)$ near a convex exposed face of $C(X)$ which does not have rank-one connections. Our estimates depend on the weak-(1,1) bounds for certain singular integral operators and the geometric features of the convex polytope $C(K)$. We show by an example that our estimate is `local' and independent of the `size' of $K$, hence it is a better estimate than the polyconvex hull $P(K)$ which is `size' dependent.
Mots-clés : Direct estimates, quasiconvex polytopes, quasiconvex envelope, singular integral operators, polyconvex hull 
K. Zhang. Estimates of Quasiconvex Polytopes in the Calculus of Variations. Journal of convex analysis, Tome 13 (2006) no. 1, pp. 37-5. http://geodesic.mathdoc.fr/item/JCA_2006_13_1_JCA_2006_13_1_a2/
@article{JCA_2006_13_1_JCA_2006_13_1_a2,
     author = {K. Zhang},
     title = {Estimates of {Quasiconvex} {Polytopes} in the {Calculus} of {Variations}},
     journal = {Journal of convex analysis},
     pages = {37--5},
     year = {2006},
     volume = {13},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_1_JCA_2006_13_1_a2/}
}
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