Abstract
Hemivariational inequalities arise e.g. in the variational formulation of boundary value problems in Mechanics and Engineering governed by nonconvex, possibly nonsmooth energy functionals (so-called superpotentials). This kind of energy functionals appear if nonmonotone, possibly multivalued constitutive laws are taken into account, cf. e.g. [17, 20, 22]. An abstract formulation of a hemivariational inequality reads as follows:
Let V be a reflexive Banach space and V* its dual, let A;V → V* be some pseudomonotone and coercive operator and let h ∈ V* be some given element.
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Carl, S. (2001). A Survey of Recent Results on the Enclosure and Extremality of Solutions for Quasilinear Hemivariational Inequalities. In: Gilbert, R.P., Panagiotopoulos, P.D., Pardalos, P.M. (eds) From Convexity to Nonconvexity. Nonconvex Optimization and Its Applications, vol 55. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0287-2_2
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