Hemivariational Inequalities. Existence and Approximation Results

  • P. D. Panagiotopoulos
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 288)


The theory of variational inequalities is closely connected to the notion of superpotential introduced by Moreau1 for convex generally non-differentiable and nonfinite energy functionals. If Φ is such a functional, a superpotential relation (material law or boundary condition) in the sense of Moreau has the form
$$f \in \partial \Phi \left( u \right)$$
where f and u are a “force” and a “flux” respectively in the terminology of Onsager’s theory and ∂ denotes the subdifferential2, which is a monotone multivalued operator. Such a law allows the derivation of variational inequalities3, 4 which are expressions of the principle of virtual or complementary virtual work (or power) in static problems and of d’ Alembert’s principle in dynamic problems.


Variational Inequality Heat Conduction Problem Hemivariational Inequality Hausdorff Topological Vector Space Multivalued Operator 


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Copyright information

© Springer-Verlag Wien 1985

Authors and Affiliations

  • P. D. Panagiotopoulos
    • 1
  1. 1.School of TechnologyAristotelian UniversityThessalonikiGreece

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