ABSTRACT
This chapter is devoted to the study of constrained problems in reflexive Banach spaces, in which the set of all admissible elements is nonconvex but star-shaped. Due to the nonconvexity of the admissible sets the corresponding variational formulations are no longer variational inequalities but, instead, take the form of hemivariational inequalities. It deals with a case in which a compactness argument is involved. This chapter is devoted to the study of variational problems involving convex lower semicontinuous functions and also the indicator functions of some closed nonconvex star-shaped sets. The results of the chapter permit the formulation and solution of many new problems in the theory of elasticity. All the problems which, the authors will study are connected with the treatment of linear elastic bodies whose displacement field or stress field is subjected to constraints expressed by means of nonconvex star-shaped and closed admissible sets.
