An Introduction to Variational Inequalities and Their Applications

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.

Preface to the SIAM edition; Preface; Glossary of notations; Introduction; Part I. Variational Inequalities in Rn; Part II. Variational Inequalities in Hilbert Space; Part III. Variational Inequalities for Monotone Operators; Part IV. Problems of Regularity; Part V. Free Boundary Problems and the Coincidence Set of the Solution; Part VI. Free Boundary Problems Governed by Elliptic Equations and Systems; Part VII. Applications of Variational Inequalities; Part VIII. A One Phase Stefan Problem; Bibliography; Index.