Variational Inequalities,Bifurcation and Applications

Although the study of variational inequalities dates back to the origins of the calculus of variations, their systematic development began in the sixties with the work of Fichera ([]) and Stampacchia ([], []), which was motivated by problems in mechanics (obstacle problems in elasticity — the Signorini problem) and potential theory (the study of the capacity of sets). After the fundamental work of Lions and Stampacchia ([]), the study of variational inequalities intensified and became an important subject in nonlinear analysis. The rapid growth of the theory was made possible by the work of Brézis ([], []), Browder ([], []), Kinderlehrer and Stampacchia ([]), Duvaut and Lions ([]),…. It brought about important contributions to nonlinear analysis, calculus of variations, optimization theory, optimal control, and to many branches of mechanics, mathematical physics, and engineering.