Contemporary Mathematics 2007; 495 pp; softcover Volume: 446 ISBN10: 0821841904 ISBN13: 9780821841907 List Price: US$133 Member Price: US$106.40 Order Code: CONM/446
 In celebration of Haïm Brezis's 60th birthday, a conference was held at the École Polytechnique in Paris, with a program testifying to Brezis's wideranging influence on nonlinear analysis and partial differential equations. The articles in this volume are primarily from that conference. They present a rare view of the state of the art of many aspects of nonlinear PDEs, as well as describe new directions that are being opened up in this field. The articles, written by mathematicians at the center of current developments, provide somewhat more personal views of the important developments and challenges. In his own work, Brezis has been a seminal influence in many important areas: critical growth in semilinear equations, variational analysis of functionals in borderline compactness cases, vector valued equations, the GinzburgLandau theory, as well as generalized degree theory and fine properties of Sobolev spaces. This same breadth is reflected in the mathematics in this collection. Researchers in nonlinear partial differential equations will find much of interest in this volume. Readership Research mathematicians interested in nonlinear partial differential equations. Table of Contents  A. Aftalion  Vortex patterns in Bose Einstein condensates
 A. Ambrosetti and A. Malchiodi  Concentration phenomena for nonlinear Schrödinger equations: Recent results and new perspectives
 L. Ambrosio, C. De Lellis, and J. Malý  On the chain rule for the divergence of \(BV\)like vector fields: Applications, partial results, open problems
 A. Bahri  Compactness
 H. Berestycki and F. Hamel  Generalized travelling waves for reactiondiffusion equations
 F. Bethuel and D. Chiron  Some questions related to the lifting problem in Sobolev spaces
 J. Bourgain  Normal forms and the nonlinear Schrödinger equation
 X. Cabré  Extremal solutions and instantaneous complete blowup for elliptic and parabolic problems
 L. A. Caffarelli and A. Mellet  Capillary drops on an inhomogeneous surface
 P. Constantin  Diffusive Lagrangian transformations, NavierStokes equations and applications
 J.M. Coron  Some open problems on the control of nonlinear partial differential equations
 L. C. Evans  The 1Laplacian, the \(\infty\)Laplacian and differential games
 J.F. Le Gall  Probabilistic approach to a class of semilinear partial differential equations
 A. Haddad and Y. Meyer  Variational methods in image processing
 S. Klainerman  Null hypersurfaces with finite curvature flux and a breakdown criterion in general relativity
 Y. Li  Some Liouville theorems and applications
 F. Lin and Y. Yang  Analysis on Faddeev knots and Skyrme solitons: Recent progress and open problems
 M. Marcus and L. Véron  The precise boundary trace of positive solutions of the equation \(\Delta u=u^q\) in the supercritical case
 H. Matano  Blowup in nonlinear heat equations with supercritical power nonlinearity
 P. Mironescu  Sobolev maps on manifolds: Degree, approximation, lifting
 P. Pucci, B. Sciunzi, and J. Serrin  Partial and full symmetry of solutions of quasilinear elliptic equations, via the comparison principle
 P. H. Rabinowitz  Single and multitransition solutions of a family of pde's
 S. Serfaty  Some methods and issues in the dynamics of vortices in the parabolic GinzburgLandau equations
