Gives a complete and rigorous presentation of the mathematical study of the expressions - hemivariational inequalities - arising in problems that involve nonconvex, nonsmooth energy functions. A theory of the existence of solutions for inequality problems involving monconvexity and nonsmoothness is established.
". . .well written and organized. . ..clearly stated. . ..provides a broader and more unified perspective on what still needs to be developed. . ..these results will be applied in the fields of mechanics, elasticity, and various branches of engineering."
Introductory material; pseudo-monotonicity and generalized pseudo-monotonicity; hemivariational inequalities for static one-dimensional nonconvex superpotential laws; hemivariational inequalities for locally Lipschitz functionals; hemivariational inequalities for multidimensional superpotential law; noncoercive hemivariational inequalities related to free boundary problems; constrained problems for nonconvex star-shaped admissible sets.