The natural best approximant in Orlicz spaces of Young measures Original Research Article

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 View the MathML source. When the function Φ0 is approached in a given way by a family of functions Φε we prove that a sequence of minimizers of the Φε-norm will converge, as ε→0, to a specific minimizer of Φ0-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.