On some computable quasiconvex multiwell functions

The translation method for constructing quasiconvex lower bound of a given function in the calculus of variations and the notion of compensated convex transforms for tightly approximate functions in Euclidean spaces will be briefly reviewed. By applying the upper compensated convex transform to the finite maximum function we will construct computable quasiconvex functions with finitely many point wells contained in a subspace with rank-one matrices. The complexity for evaluating the constructed quasiconvex functions is O(k log k) with k the number of wells involved. If time allows, some new applications of compensated convexity will be briefly discussed.