On May 11, 2012, Professor Patrizia Pucci turned 60. In celebration of Patrizia
Pucci’s birthday, a conference was held at the University of Perugia during May 28
and June 1, 2012. The main purpose of this scientific meeting has been to bring
together leading experts and researchers in nonlinear partial differential equations,
to promote research and to stimulate interactions among the participants. An
atmosphere of particular warmth and the high scientific level made this conference
memorable. The program testified to the wide ranging influence of Professor Pucci
on the field of nonlinear analysis and partial differential equations. Many of the
speakers also spoke about the generosity of Patrizia in welcoming and encouraging
young new researchers.
In her own work, Patrizia Pucci has been a seminal influence in many important
areas: the maximum principle, qualitative analysis of solutions to many classes
of nonlinear PDEs (Kirchhoff problems, polyharmonic systems), mountain pass
theorem in the critical case, critical exponents, variational identities, as well as
various degenerate or singular phenomena in mathematical physics. This same
breadth is reflected in the mathematical papers included in these two volumes.
The articles in these volumes are primarily from the conference held in Perugia.
They present an original view of the state of the art of many aspects of nonlinear
partial differential equations. The articles, written by mathematicians at the center
of current developments, provide somewhat more personal views of the important
developments and challenges. The first volume contains contributions on the field
of nonlinear evolution partial differential equations. The first contribution to this
volume is a typed version of the slides Professor James Serrin used in the opening
conference of the workshop.
We are delighted that these two volumes appear in the prestigious Contempo-
rary Mathematics Series of the American Mathematical Society. We are grateful
to Sergei Gelfand, the AMS Book Program Publisher, who gave his wholehearted
support to this project. We address special thanks to Christine Thivierge for her
professional guidance throughout the publication process.
Enzo L. Mitidieri
Vicent ¸iu D. R˘adulescu