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Weak Convergence Methods for Nonlinear Partial Differential Equations
Lawrence C. Evans, University of California, Berkeley, CA
A co-publication of the AMS and CBMS.
cover
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CBMS Regional Conference Series in Mathematics
1990; 82 pp; softcover
Number: 74
Reprint/Revision History:
1990, fourth printing 1996
ISBN-10: 0-8218-0724-2
ISBN-13: 978-0-8218-0724-8
List Price: US$19
Member Price: US$15.20
All Individuals: US$15.20
Order Code: CBMS/74
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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

  • Weak convergence
  • Convexity
  • Quasiconvexity
  • Concentrated compactness
  • Compensated compactness
  • Maximum principle methods
  • Appendix
  • Notes
  • References
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