We use W1,∞ approximations of minimizing sequences to study the growth of some quasiconvex functions near their zero sets. We show that for SO(n), the quasiconvexification of the distance function dist2(·, SO(n)) can be bounded below by the distance function itself. In certain cases of the incompatible two elastic well structure, we establish a similar result. We also prove that for small Lipschitz perturbations of SO(n) and of the two well structure, the Young measure limits of gradients supported on these perturbed sets are Dirac masses.
Cite this article
Kewei Zhang, Quasiconvex functions, SO(n) and two elastic wells. Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997), no. 6, pp. 759–785DOI 10.1016/S0294-1449(97)80132-1