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The 9th Conference on Free Boundary Problems was held in Trento in June 5-8, 2002. This meeting gathered 159 participants from 22 different countries including Argentina, Cuba, China, Japan, Saudi Arabia, Taiwan. The conference registered 20 plenary lectures given by leading scientist in the fields of modelling, analysis and numerical treatment of PDE's, along with 7 focus sessions with three or four speakers each and a poster session with 64 contributions. In the opinion of most of attending people, the conference was a major event with a large success.

Free boundary problems arise naturally in differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary"; a further quantitative condition must be then provided to exclude undeterminacy.

Problems of this sort arise in a large number of phenomena of applicative interest. Examples include the classic Stefan problem, and more general models of phase transitions: here the free boundary is represented by the moving interface between phases. Other important examples occur in filtration through porous media; here free boundaries occur as fronts between saturated and unsaturated regions. Relevant examples come from reaction-diffusion, fluid dynamics, and so on.

Free boundaries are often related to discontinuities in constitutive relations; this raises a number of interesting analytic and numerical questions. Existence of the solution in function spaces, uniqueness, regularity properties, numerical approximation procedures, and other questions have been extensively investigated. The interested reader is referred to the proceedings of the previous editions of the series of FBP conferences. Several of these problems are of industrial interest, and offer opportunities of collaboration among mathematicians, physicists, engineers, material scientists, and other applicative scientists.

A large community of mathematicians, engineers and applicative scientists spread over the world has been formulating and studying free boundary problems for many years, and has been meeting regularly in a major conference any third year or so. Actually, a list of previous editions of this series of meetings is

* 1981 Montecatini (Italy)
* 1984 Maubuissons (France)
* 1987 Irsee (Germany)
* 1990 Montreal (Canada)
* 1993 Toledo (Spain)
* 1995 Zakopane (Poland)
* 1997 Crete (Greece)
* 1999 Chiba (Japan)

Following the tradition of the series, the 2002 conference on Free Boundary Problems was organized in Trento in the period June 5-8, 2002, by collecting the joint efforts of an italian-german partnership which involved Pierluigi Colli, Gerhard Dziuk, Antonio Fasano, Karl-Heinz Hoffmann, Jürgen Sprekels, Claudio Verdi, Augusto Visintin as direct and contributing organizers.

The scientific committee included Michel Frémond (Paris), Avner Friedman (Columbus, Ohio), Stephan Luckhaus (Leipzig), Marek Niezgodka (Warsaw), John R. Ockendon (Oxford), Mario Primicerio (Firenze) and José Francisco Rodrigues (Lisboa).

Topics covered at the Trento conference concerned problems which are more or less directly related to free boundaries, or might be so in perspective. Special emphasis has been put on questions of applicative relevance: in particular, there has been a special focus on modelling, new phenomenology, analysis of related mathematical problems, qualitative properties of solutions, numerical issues. The list of participants was made up of not only mathematicians but engineers, physicists, and other applicative scientists.

To give a precise report on the topics issued and discussed during the conference, let us detail the titles of the 20 plenary lectures, in alphabetic order of speakers,

1. Gregoire Allaire: Structural optimization by the level set method.
2. Luigi Ambrosio: Non linear function spaces associated to singular perturbations.
3. Giorgio Bertotti: Magnetization modes and spin-wave instabilities in nonlinear magnetization dynamics.
4. Zhiming Chen: Upscaling of well singularities of flow transport through heterogeneous porous media.
5. Pierre Degond: A model for the plasma-vacuum interface.
6. Emmanuele DiBenedetto: On the selection problem for the Hele-Show flow.
7. Wolfgang Dreyer: On nucleation and growth of liquid droplets in single crystals.
8. Martin E. Glicksman: Dendritic growth & melting in pure systems.
9. Nobuyuki Kenmochi: Transmission-Stefan problems arising in Czochralski process of crystal growth.
10. Robert Kohn: Upper bounds on coarsening rates.
11. Stefan Müller: Multiscale folding patterns and energy scaling in compressed thin films.
12. Ricardo H. Nochetto: A posteriori error control of FBPs.
13. Felix Otto: Scaling laws for the cross--tie wall.
14. Oliver Penrose: Diffusion-induced grain boundary motion : a system with three free boundaries.
15. Errico Presutti: Phase coexistence and interfaces in statistical mechanics.
16. Alfio Quarteroni: Fluid dynamics in blood circulation.
17. Fernando Reitich: Shape deformations and analytic continuation in free boundary problems.
18. Alfred Schmidt: Adaptive finite element methods for phase transition computations.
19. Victor N. Zur Starovoitov: Penalty method and problems of liquid - solid interaction.
20. Juan José López Velazquez: Some mathematical questions on fracture dynamics.

and the 7 focus sessions with their organizers

1. Vincenzo Capasso: Free boundary problems in polymer science, including Martin Burger, Alessandra Micheletti and Riccardo Ricci as speakers.
2. Vicent Caselles: Image processing, including Simon Masnou, Matteo Novaga and Andrés F. Solé Martínez as speakers.
3. Charles M. Elliott: Grain boundary motion, including Kazuo Ito, Barbara Niethammer and Vanessa Styles as speakers.
4. Ralph Kornhuber: Numerical aspects of free boundary problems, including Eberhard Baensch, Folkmar A. Bornemann and Giuseppe Savarè as speakers.
5. Masayasu Mimura: Free boundary problems in biomathematics, including Elaine Crooks, Danielle Hilhorst and Boris Zaltzman as speakers.
6. Georg Müller: Modelling in crystal growth, including Jeffrey J. Derby, Michael Metzger, H.S. Udaykumar, and Georg Mueller as speakers.
7. Peter Bates: Transitions in anisotropic materials, including Stephen Watson, Giorgio Fusco and Adam Wheeler as speakers.

The 159 participants came from 22 different countries, with a rather consistent participation of people from Italy, Germany, Japan, USA, France, Britain, in particular.

The organization and success of such a big conference has been made possible thanks to a number of supporting institutions which are mentioned here:

Universities of Trento, Milan, Florence, Freiburg i. Br., Pavia C.A.E.S.A.R. Institut of Bonn, W.I.A.S. Institut of Berlin Projects "Free Boundary Problems", "Scientific Computing: ...", "Symmetries, Geometric Structures, ..." of M.I.U.R. G.N.A.M.P.A., G.N.C.S., G.N.F.M. of I.N.dA.M.

Proceedings of the conference will appear in the series Internat. Ser. Numer. Math. by Birkhäuser.

Further information on the conference, including program, list of posters, participants and all abstracts can be found on the web page

fbp2002.science.unitn.it

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