CBMS Regional Conference Series in Mathematics 1990; 82 pp; softcover Number: 74 Reprint/Revision History: 1990, fourth printing 1996 ISBN10: 0821807242 ISBN13: 9780821807248 List Price: US$20 Member Price: US$16 All Individuals: US$16 Order Code: CBMS/74
 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 lowamplitude, highfrequency 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
