Elliptic and Parabolic Problems : A Special Tribute to the Work of Haim Brezis C. Bandle et al., eds. Progress in Nonlinear Differential Equations and Their Applications 63, Birkhauser (2005) 470 pp., price USD 179.00 ISBN: 3764372494
Reviewer: R. Ghrist, University of Illinois, Urbana-Champaign, USA.

Level: intermediate.

This text is a compendium of brief articles celebrating the work of H. Brezis on the occasion of his 60^th birthday. The editors of this volume are Catherine Bandle, Henri Berestycki, Bernhard Brighi, Alain Brillard, Michel Chipot, Jean-Michel Coron, Carlo Sbordone, Itai Shafrir, Vanda Valente, and Giorgio Vergara Caffarelli.

It is a testimony to the breadth and impact of Brezis' work that a celebratory book contains 44 articles. The articles span a wide range of topics, including boundary layers, similarity solutions, surface meshing and parameterization, 3-body problems, PDEs on fractal domains, and numerical methods for PDEs. Researchers in mathematical techniques for PDEs will find a wealth of interesting and technical material. In addition, researchers who are more inclined to applications of PDEs will find articles on bifurcation theory, heat transfer, fluid dynamics, convection, porous media, gas dynamics, and membranes.

The articles are on average brief, introductory, and informative. While the text is not appropriate for a course or for reading front-to-back, it nevertheless would be an interesting and informative read for anyone working on nearly any aspect of PDEs. The only thing lacking in this volume is a comprehensive historical treatment of Brezis' work. Any reader interested in such a treatment will have to suffice with reading the list of 44 titles.