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A Class of Subdifferential Inclusions for Elastic Unilateral Contact Problems

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Abstract

We consider a class of stationary subdifferential inclusions in a reflexive Banach space. We reformulate the problem in terms of a variational inequality with multivalued term and prove an existence result using the Kakutani-Fan-Glicksberg fixed point theorem. This approach allows to consider, in a natural way, a dual variational formulation of the problem. Next, we study the link between the primal and dual formulations and provide an equivalence result. Then, we consider a new mathematical model which describes the contact of an elastic body with a foundation. We apply the abstract formalism to derive the primal and the dual variational formulations of the problem, in terms of displacement and stress, respectively. Finally, we present existence and equivalence results in the study of this contact model.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Jagiellonian University in Krakow, ul. Łojasiewicza 6, 30348, Krakow, Poland

    Piotr Kalita & Stanisław Migórski

  2. Laboratoire de Mathématiques et Physique, Université de Perpignan Via Domitia, 52 Avenue Paul Alduy, 66860, Perpignan, France

    Mircea Sofonea

Authors
  1. Piotr Kalita
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  2. Stanisław Migórski
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  3. Mircea Sofonea
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Correspondence to Mircea Sofonea.

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Kalita, P., Migórski, S. & Sofonea, M. A Class of Subdifferential Inclusions for Elastic Unilateral Contact Problems. Set-Valued Var. Anal 24, 355–379 (2016). https://doi.org/10.1007/s11228-015-0346-3

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  • DOI: https://doi.org/10.1007/s11228-015-0346-3

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