Perspectives in Nonlinear Partial Differential Equations: In Honor of Haïm Brezis
About this Title
Henri Berestycki, Michiel Bertsch, Felix E. Browder, Louis Nirenberg, Lambertus A. Peletier and Laurent Véron, Editors
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
- Amandine Aftalion – Vortex patterns in Bose Einstein condensates [MR 2373722]
- Antonio Ambrosetti and Andrea Malchiodi – Concentration phenomena for nonlinear Schrödinger equations: recent results and new perspectives [MR 2373723]
- Luigi Ambrosio, Camillo De Lellis and Jan Malý – On the chain rule for the divergence of BV-like vector fields: applications, partial results, open problems [MR 2373724]
- A. Bahri – Compactness [MR 2373725]
- Henri Berestycki and François Hamel – Generalized travelling waves for reaction-diffusion equations [MR 2373726]
- Fabrice Bethuel and David Chiron – Some questions related to the lifting problem in Sobolev spaces [MR 2373727]
- J. Bourgain – Normal forms and the nonlinear Schrödinger equation [MR 2373728]
- Xavier Cabré – Extremal solutions and instantaneous complete blow-up for elliptic and parabolic problems [MR 2373729]
- L. A. Caffarelli and A. Mellet – Capillary drops on an inhomogeneous surface [MR 2373730]
- Peter Constantin – Diffusive Lagrangian transformations, Navier-Stokes equations and applications [MR 2373731]
- Jean-Michel Coron – Some open problems on the control of nonlinear partial differential equations [MR 2376661]
- Lawrence C. Evans – The 1-Laplacian, the $\infty $-Laplacian and differential games [MR 2376662]
- Jean-François Le Gall – Probabilistic approach to a class of semilinear partial differential equations [MR 2376663]
- Ali Haddad and Yves Meyer – Variational methods in image processing [MR 2376664]
- Sergiu Klainerman – Null hypersurfaces with finite curvature flux and a breakdown criterion in general relativity [MR 2376665]
- YanYan Li – Some Liouville theorems and applications [MR 2376666]
- Fanghua Lin and Yisong Yang – Analysis on Faddeev knots and Skyrme solitons: recent progress and open problems [MR 2376667]
- Moshe Marcus and Laurent Veron – The precise boundary trace of positive solutions of the equation $\Delta u=u^q$ in the supercritical case [MR 2376668]
- Hiroshi Matano – Blow-up in nonlinear heat equations with supercritical power nonlinearity [MR 2376669]
- Petru Mironescu – Sobolev maps on manifolds: degree, approximation, lifting [MR 2376670]
- Patrizia Pucci, Berardino Sciunzi and James Serrin – Partial and full symmetry of solutions of quasilinear elliptic equations, via the comparison principle [MR 2376671]
- Paul H. Rabinowitz – Single and multi-transition solutions of a family of PDEs [MR 2376672]
- Sylvia Serfaty – Some methods and issues in the dynamics of vortices in the parabolic Ginzburg-Landau equations [MR 2376673]
- Henri Berestycki, Michiel Bertsch, Felix E. Browder, Louis Nirenberg, Lambertus A. Peletier and Laurent Véron – Publications of Haïm Brezis [MR 2376734]