Iterated function systems and stability of variational problems on self-similar objects (Q619738)

From the text: ``Many physical phenomena can be described by variational problems. Classical models and techniques to solve these kinds of problems rely on the assumption that a gradient (maybe in some generalized form is defined and that the underlying domain is smooth. However, non-smooth structures appear frequently in physical phenomena creating `irregular' and `rough' objects.'' In this paper, the authors consider a variational optimization problem involving multifunctions, and prove in Theorem 2 a stability result with respect to the Monge-Kantorovich metric. They then apply Theorem 2 to variational problems of the kind above; namely, to variational problems in which the functional is defined on fractals generated by iterated function systems (Corollary~4).