We show that for any compact set K ? MN×n, LC(K) = C(K) if and only if Q(K) = C(K), LC(K), Q(K) and C(K) being the closed lamination convex hull, quasiconvex hull and convex hull of K respectively. When K ? M2×2, we show that LC(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.
|Number of pages||18|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 1998|