The goal of these proceedings and of the meeting of Gaeta was to celebrate and honor the mathematical achievements of Haim Brezis. The prodigious inﬂuence of his talent and his personality in the domain of nonlinear analysis is unanimously acclaimed! This impact is visible in the huge number of his former students (dozens), students of former students (hundreds) and collaborators (hundreds). Thus the Gaeta meeting was, to some extent, the family reunion of part of this large community sharing a joint interest in the ﬁeld of elliptic and parabolic equations and pushing it to a very high standard.
Italy has a long tradition and taste for analysis and we could not ﬁnd a better place neither a more complete support for the realisation of our pro ject. We have to thank here the university of Cassino, Napoli, Roma “la Sapienza”, the GNAMPA-Istituto di Alta Matematica, CNR-IAC, MEMOMAT, RTN Fronts-Singularities, the commune of Gaeta. Additional founding came from the universities of Mulhouse and Zurich. Finally, we are grateful to Birkh¨
auser and Dr. Hempﬂing who allowed us to record the talks of this conference in a prestigious volume.