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

Voir la notice de l'article provenant de la source Heldermann Verlag

\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 
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     author = {K. Zhang},
     title = {Estimates of {Quasiconvex} {Polytopes} in the {Calculus} of {Variations}},
     journal = {Journal of convex analysis},
     pages = {37--5},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2006},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_1_JCA_2006_13_1_a2/}
}
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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/