Boundary Values in the Geometric Function Theory in Domains with Moving Boundaries

This article addresses the problem of boundary correspondencefor a sequence of homeomorphisms thatchange the capacity of a condenser in a controlled way.To study the overall boundary behavior of these mappings,we introduce some capacity metricsin a sequence of domains with nondegenerate core.Completions with respect to these metrics add to the domains new points called boundary elements.As one of the consequences, we obtain not only sufficient conditions forthe global uniform convergence of a sequence of homeomorphisms,but some applications to elasticity theory as well.