ON VARIOUS SEMICONVEX HULLS IN THE CALCULUS OF VARIATIONS

We show that for any compact set K subset of M-Nxn, L-c(K) = C(K) if a nd only if Q(K) = C(K), L-c(K), Q(K) and C(K) being the closed laminat ion convex hull, quasiconvex hull and convex hull of K respectively. W hen K subset of M-2x2 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 function s.