Weak Convergence Methods for Nonlinear Partial Differential Equations

Lawrence C. Evans

ISBN 10: 0821807242 / ISBN 13: 9780821807248

Published by American Mathematical Society, US, 1990

About this Item

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.

Seller Inventory # LU-9780821807248

Bibliographic Details

• Title: Weak Convergence Methods for Nonlinear Partial Differential Equations
• Publisher: American Mathematical Society, US
• Publication Date: 1990
• Language: English
• ISBN 10: 0821807242
• ISBN 13: 9780821807248
• Binding: Paperback
• Condition: New
• Dimensions: 17.78W x 0.64H x 25.4D centimeters 17.78 centimeters width by 0.64 centimeters height by 25.4 centimeters depth
• Weight: 181 grams

About this title

Synopsis

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 at the forefront of this vital area of research