Volume: 74; 1990; 82 pp; Softcover
MSC: Primary 35; 46; Secondary 58
Print ISBN: 978-0-8218-0724-8
Product Code: CBMS/74
List Price: $22.00
Individual Price: $17.60
Electronic ISBN: 978-1-4704-2434-3
Product Code: CBMS/74.E
List Price: $20.00
Individual Price: $16.00
Weak Convergence Methods for Nonlinear Partial Differential Equations
Share this pageLawrence C. Evans
A co-publication of the AMS and CBMS
The purpose of this book is to explain systematically
and clearly many of the most important techniques set forth in
recent years for using weak convergence methods to study nonlinear
partial differential equations. This work represents an expanded version
of a series of ten talks presented by the author at Loyola University
of Chicago in the summer of 1988.
The author surveys a wide collection of techniques for showing
the existence of solutions to various nonlinear partial
differential equations, especially when strong analytic estimates are
unavailable. The overall guiding viewpoint is that when a sequence of
approximate solutions converges only weakly, one must exploit the
nonlinear structure of the PDE to justify passing to limits. The
author concentrates on several areas that are rapidly developing and
points to some underlying viewpoints common to them all. Among the
several themes in the book are the primary role of measure theory and
real analysis (as opposed to functional analysis) and the continual use
in diverse settings of low-amplitude, high-frequency periodic
test functions to extract useful information. The author uses the
simplest problems possible to illustrate various key techniques.
Aimed at research mathematicians in the field of nonlinear PDEs, this
book should prove an important resource for understanding the techniques
being used in this important area of research.
Readership
Mathematicians in the field of nonlinear PDEs.
Table of Contents
Table of Contents
Weak Convergence Methods for Nonlinear Partial Differential Equations
- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents v6 free
- Preface vii8 free
- Introduction 110 free
- 1. Weak Convergence 413 free
- 2. Convexity 1827
- 3. Quasiconvexity 2231
- 4. Concentrated Compactness 3443
- 5. Compensated Compactness 4958
- 6. Maximum Principle Methods 6675
- Appendix 7584
- Notes 7685
- References 7887
- Back Cover Back Cover195