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

  • Siegfried Carl
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 55)


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;VV* be some pseudomonotone and coercive operator and let hV* be some given element.


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Siegfried Carl
    • 1
  1. 1.Fachbereich Mathematik und Informatik, Institut für AnalysisMartin-Luther-Universität Halle-WittenbergHalleGermany

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