On June 1, 2004, Ha!m Brezis turned 60, an occasion that was celebrated by
scientific conferences held in the USA, Italy and France. The Carre des Sciences
in the old building of the Ecole Polytechnique, now the Ministere de la Recherche,
provided a fitting backdrop for the Paris meeting, which was held on June 21-25,
2004. An atmosphere of personal warmth and the scientific breadth and depth
made this occasion memorable. The program testified to the wide ranging influ-
ence of Haim on the field of nonlinear analysis and partial differential equations.
In particular, his unique role in stimulating research and opening new directions
was emphasized. Many lecturers had the occasion to recall Ha!m's special passion
and talent for open problems and his continuous un-abiding discoveries of gem-like
challenging questions. Many of the speakers also spoke of the generosity of Haim
in welcoming and encouraging young new researchers.
As a tribute paid to Haim Brezis, the lecturers at the Paris meeting made a
particular effort to put together a rare view of the state of the art of many aspects
of nonlinear partial differential equations, as well as to describe new directions that
are being opened up in this field, and some of the challenges it faces.
In the same spirit, it was felt that such perspectives should be gathered and
recorded through a collection of articles that make up this volume. Written by
mathematicians at the center of current developments, many of whom spoke at the
Paris meeting, this volume provides somewhat more personal views of the important
directions and challenges.
The American Mathematical Society responded with enthusiasm to this project
and supported it with high-quality professionnal help. We are delighted that this
volume appears in the scientifically-demanding Contemporary Mathematics Series.
It is with pleasure that we offer thanks to the publishing team of the AMS, in
particular to Edward Dunne and Christine Thivierge. We also wish to express
our thanks to Ann Kostant of Birkauser, Boston, who was very supportive of the
Besides the mathematical articles, two memorable speeches have been tran-
scribed and included here, at the beginning of this volume. They were delivered by
Haim and by Michal Govrin, his wife, a Hebrew writer, at a party in honor of Haim
during the meeting in Paris. They convey something of the special atmosphere of
this meeting. We are grateful to them for granting us permission to print these
personal thoughts in this volume.