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Noncoercive Variational–Hemivariational Inequalities: Existence, Approximation by Double Regularization, and Application to Nonmonotone Contact Problems

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Abstract

We study noncoercive nonlinear variational–hemivariational inequalities that encompass semicoercive nonlinear monotone variational inequalities and pseudomonotone variational inequalities in reflexive Banach spaces, respectively, hemivariational inequalities in function spaces. We present existence and approximation results. Our approach consists in a double regularization: we combine a Browder–Tikhonov regularization with regularization tools of nondifferentiable optimization to smooth the jumps in the hemivariational term. As application, we treat a noncoercive unilateral contact problem in continuum mechanics with nonmonotone friction.

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Acknowledgements

The authors would like to thank the anonymous referees whose insightful comments have benefited the contents of this article.

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Authors and Affiliations

  1. Ibn Zohr University, Agadir, Morocco

    Ouayl Chadli

  2. Universität der Bundeswehr München, Neubiberg, Germany

    Joachim Gwinner

  3. University of Central Florida, Orlando, FL, USA

    M. Zuhair Nashed

Authors
  1. Ouayl Chadli
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  2. Joachim Gwinner
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  3. M. Zuhair Nashed
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Correspondence to Joachim Gwinner.

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Communicated by Jan Sokolowski.

Dedicated to Professor Franco Giannessi on the occasion of his 85th birthday.

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Chadli, O., Gwinner, J. & Nashed, M.Z. Noncoercive Variational–Hemivariational Inequalities: Existence, Approximation by Double Regularization, and Application to Nonmonotone Contact Problems. J Optim Theory Appl 193, 42–65 (2022). https://doi.org/10.1007/s10957-022-02006-1

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