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Perspectives in Nonlinear Partial Differential Equations: In Honor of Haïm Brezis
Edited by: Henri Berestycki, École des Hautes Études en Sciences Sociales, Paris, France, Michiel Bertsch, Università di Roma "Tor Vergata", Rome, Italy, Felix E. Browder, Rutgers University, New Brusnwick, NJ, Louis Nirenberg, New York University - Courant Institute, NY, Lambertus A. Peletier, Leiden University, The Netherlands, and Laurent Véron, Université François Rabelais, Tours, France

Contemporary Mathematics
2007; 495 pp; softcover
Volume: 446
ISBN-10: 0-8218-4190-4
ISBN-13: 978-0-8218-4190-7
List Price: US$133
Member Price: US$106.40
Order Code: CONM/446
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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 wide-ranging 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 semi-linear equations, variational analysis of functionals in borderline compactness cases, vector valued equations, the Ginzburg-Landau 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.


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 reaction-diffusion 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 blow-up for elliptic and parabolic problems
  • L. A. Caffarelli and A. Mellet -- Capillary drops on an inhomogeneous surface
  • P. Constantin -- Diffusive Lagrangian transformations, Navier-Stokes equations and applications
  • J.-M. Coron -- Some open problems on the control of nonlinear partial differential equations
  • L. C. Evans -- The 1-Laplacian, 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 -- Blow-up 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 multi-transition solutions of a family of pde's
  • S. Serfaty -- Some methods and issues in the dynamics of vortices in the parabolic Ginzburg-Landau equations
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