The present volume contains the proceedings of the workshop on "Minimax
Theory and Applications" that was held during the week 30 September - 6
October 1996 at the "G. Stampacchia" International School of Mathematics
of the "E. Majorana" Centre for Scientific Cul- ture in Erice (Italy) .
The main theme of the workshop was minimax theory in its most classical
meaning. That is to say, given a real-valued function f on a product
space X x Y, one tries to find conditions that ensure the validity of
the equality sup inf f(x, y) = inf sup f(x, y). yEY xEX xEX yEY This is
not an appropriate place to enter into the technical details of the
proofs of minimax theorems, or into the history of the contribu- tions
to the solution of this basic problem in the last 7 decades. But we do
want to stress its intrinsic interest and point out that, in spite of
its extremely simple formulation, it conceals a great wealth of ideas.
This is clearly shown by the large variety of methods and tools that
have been used to study it. The applications of minimax theory are also
extremely interesting. In fact, the need for the ability to "switch
quantifiers" arises in a seemingly boundless range of different
situations. So, the good quality of a minimax theorem can also be judged
by its applicability. We hope that this volume will offer a rather
complete account of the state of the art of the subject.