The natural best approximant in Orlicz spaces of Young measures

This paper is dealing with the problem of existence and uniqueness of the natural minimizer of a convex set in a Orlicz class of Young measures, say Y-Phi0. When the function Phi(0) is approached in a given way by a family of functions Phi(epsilon) we prove that a sequence of minimizers of the Phi(epsilon)-nonn will converge, as epsilon --> 0, to a specific minimizer of Phi(0)-norm, which can also be found solving a minimizing problem in another Orlicz class of Young measure. The present paper extends the similar results existing in the literature, on natural best approximation in Orlicz classes of functions, and in integrable families of Young measures. (C) 2004 Elsevier Ltd. All rights reserved.