APPROXIMATION OF YOUNG MEASURES BY FUNCTIONS AND APPLICATION TO A PROBLEM OF OPTIMAL-DESIGN FOR PLATES WITH VARIABLE THICKNESS

Given a parametrised measure and a family of continuous functions (phi (n)), we construct a sequence of functions (u(k)) such that, as k --> infinity, the functions phi(n)(u(k)) converge to the corresponding mom ents of the measure, in the weak topology. Using the sequence (u(k)) corresponding to a dense family of continuous functions, a proof of t he fundamental theorem for Young measures is given. We apply these tec hniques to an optimal design problem for plates with variable thicknes s. The relaxation of the compliance functional involves three continuo us functions of the thickness. We characterise a set of admissible gen eralised thicknesses, on which the relaxed functional attains its mini mum.