Minimax balayage theorem and an inscribed ball problem (Q1060405)

A balayage theorem is a result which makes it possible in a certain sense to shrink (''balayer'') the region of optimization of a given functional without changing the optimal value. Such results go back to a well-known theorem of de la Vallée-Poussin and have been studied by numerous workers. The goals of this paper are the following: 1) to focus attention on the dual nature of balayage, which shows up in a number of important cases; 2) to carry over balayage theorems to cover certain nonconvex problems; 3) to consider the ''inscribed'' ball problem as an example.