An Introduction to Variational Inequalities and Their Applications (Classics in Applied Mathematics, Series Number 31)

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.

David Kinderlehrer is a Professor in the Department of Mathematical Sciences at Carnegie Mellon University in Pittsburgh, Pennsylvania. He is a well-known expositor of issues at the scientific frontier of applied mathematics. His present interests focus on mesoscale phenomena, ranging from liquid crystals and microstructure in solids to protein motors, or energy transduction in molecular level processes.

Guido Stampacchia (1922-1978) profoundly influenced the development of partial differential equations and the calculus of variations. He was one of the original founders of variational inequalities and is responsible for many of the methods we still use today. He was Professor Kinderlehrer's mentor at Scuola Normale Superiore, Pisa.