An Elastic Frictional Contact Problem with Unilateral Constraint

  • Maxime Couderc
  • Mircea SofoneaEmail author


We consider a mathematical model which describes the equilibrium of an elastic body in contact with two obstacles. We derive its weak formulation which is in a form of an elliptic quasi-variational inequality for the displacement field. Then, under a smallness assumption, we establish the existence of a unique weak solution to the problem. We also study the dependence of the solution with respect to the data and prove a convergence result. Finally, we consider an optimization problem associated with the contact model for which we prove the existence of a minimizer and a convergence result, as well.


Elastic material Frictional contact Quasi-variational inequality Weak solution Convergence results Optimization problem 

Mathematics Subject Classification

74M10 74M15 49J40 49J45 49J20 


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et PhysiqueUniversity of Perpignan Via DomitiaPerpignanFrance

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