An Introduction to Variational Inequalities and Their Applications

David Kinderlehrer, Guido Stampacchia9780898714661, 0898714664

This unabridged republication of the 1980 text, an established classic in the field, is a resource for many important topics in elliptic equations and systems and is the first modern treatment of free boundary problems. Variational inequalities (equilibrium or evolution problems typically with convex constraints) are carefully explained in An Introduction to Variational Inequalities and Their Applications. They are shown to be extremely useful across a wide variety of subjects, ranging from linear programming to free boundary problems in partial differential equations. Exciting new areas like finance and phase transformations along with more historical ones like contact problems have begun to rely on variational inequalities, making this book a necessity once again.

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Table of contents :
An Introduction to Variational Inequalities and Their Applications……Page 1
Contents……Page 10
Preface to the Classics Edition……Page 14
Preface……Page 18
Glossary of Notations……Page 20
Introduction……Page 22
CHAPTER I Variational Inequalities in RN……Page 28
CHAPTER II Variational Inequalities in Hilbert Space……Page 44
CHAPTER III Variational Inequalities for Monotone Operators……Page 104
CHAPTER IV Problems of Regularity……Page 126
CHAPTER V Free Boundary Problems and the Coincidence Set of the Solution……Page 170
CHAPTER VI Free Boundary Problems Governed by Elliptic Equations and Systems……Page 205
CHAPTER VII Applications of Variational Inequalities……Page 243
CHAPTER VIII A One Phase Stefan Problem……Page 299
Bibliography……Page 321
Index……Page 330