Minimization of superposition functionals (Q1842447)

Theoretical and applied research often requires minimizing the functionals \(J(u)= L({\mathfrak R}(u))\) which are a superposition of a real function \(L\) and a multivalued mapping \(\mathfrak R\). In this paper, we study the functional-topological properties of the multivalued mappings \(\mathfrak R\) and functions \(L\) which are necessary for some extremal properties of the functional \(J\). Our results generalize and refine the studies of previous papers and have been partially announced in Dokl. Akad. Nauk, Ross. Akad. Nauk 329, No. 6, 701-704 (1993; Zbl 0814.49004)].