A Survey of Recent Results on the Enclosure and Extremality of Solutions for Quasilinear Hemivariational Inequalities
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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