**Contemporary Mathematics**

Volume: 446;
2007;
495 pp;
Softcover

MSC: Primary 35; 26; 34; 46; 49; 68; 93;

Print ISBN: 978-0-8218-4190-7

Product Code: CONM/446

List Price: $133.00

Individual Member Price: $106.40

**Electronic ISBN: 978-0-8218-8125-5
Product Code: CONM/446.E**

List Price: $133.00

Individual Member Price: $106.40

# Perspectives in Nonlinear Partial Differential Equations: In Honor of Haïm Brezis

Share this page *Edited by *
*Henri Berestycki; Michiel Bertsch; Felix E. Browder; Louis Nirenberg; Lambertus A. Peletier; Laurent Véron*

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.

#### Table of Contents

# Table of Contents

## Perspectives in Nonlinear Partial Differential Equations: In Honor of Haim Brezis

- Contents v6 free
- Preface vii8 free
- On Haïm Brézis ix10 free
- Speech of Haïm Brézis xvii18 free
- Speech of Michal Govrin xxi22 free
- Vortex patterns in Bose Einstein condensates 126 free
- Concentration phenomena for Nonlinear Schrödinger Equations: recent results and new perspectives 1944
- On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems 3156
- Compactness 6994
- Generalized travelling waves for reaction-diffusion equations 101126
- Some questions related to the lifting problem in Sobolev spaces 125150
- Normal forms and the nonlinear Schrödinger equation 153178
- Extremal solutions and instantaneous complete blow-up for elliptic and parabolic problems 159184
- Capillary drops on an inhomogeneous surface 175200
- Diffusive Lagrangian transformations, Navier-Stokes equations and applications 203228
- Some open problems on the control of nonlinear partial differential equations 215240
- The 1-Laplacian, the ∞-Laplacian and differential games 245270
- Probabilistic approach to a class of semilinear partial differential equations 255280
- Variational methods in image processing 273298
- Null hypersurfaces with finite curvature flux and a breakdown criterion in general relativity 297322
- Some Liouville theorems and applications 313338
- Analysis on Faddeev knots and Skyrme solitons: recent progress and open problems 319344
- The precise boundary trace of positive solutions of the equation ∆u = uq in the supercritical case 345370
- Blow-up in nonlinear heat equations with supercritical power nonlinearity 385410
- Sobolev maps on manifolds: degree, approximation, lifting 413438
- Partial and full symmetry of solutions of quasilinear elliptic equations via the comparison principle 437462
- Single and multi-transition solutions of a family of PDE's 445470
- Some methods and issues in the dynamics of vortices in the parabolic Ginzburg-Landau equations 459484
- Publications of Haïm Brezis 485510

#### Readership

Research mathematicians interested in nonlinear partial differential equations.