Subdifferentiability and inf-sup theorems (Q1961279)

The authors present an abstract set of hypotheses yielding the equality \[ \underset{y\in Y}{\text{Sup}} \underset{x\in X} {\text{Inf}} L(x,y)= \underset{x\in X} {\text{Inf}} \underset{y\in Y} {\text{Sup}} L(x,y), \] where \(L\) is an extended-real-valued function defined on the Cartesian product \(X\times Y\). The main feature of their minimax result is the lack of compactness assumptions, something which is compensated here with a suitable ``qualification condition'' of the Attouch-Brezis type.