Regularization of Brézis pseudomonotone variational inequalities


In this paper we prove the existence of solutions of regularized set-valued variational inequalities involving Brézis pseudomonotone operators in reflexive and locally uniformly convex Banach spaces. By taking advantage of this result, we approximate a general set-valued variational inequality with suitable regularized set-valued variational inequalities, and we show that their solutions weakly converge to a solution of the original one. Furthermore, by strengthening the coercivity conditions, we can prove the strong convergence of the approximate solutions.

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We would like to express our gratitude to the referees for their careful reading which improved the presentation of the paper. The research of the second author was supported by a Grant of the Romanian Ministry of Research and Innovation, CNCS-UEFISCDI, Project PN-III-P4-ID-PCE-2016-0190, within PNCDI III.

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Correspondence to M. Bianchi.

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Bianchi, M., Kassay, G. & Pini, R. Regularization of Brézis pseudomonotone variational inequalities. Set-Valued Var. Anal 29, 175–190 (2021).

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  • Set-valued variational inequality
  • B-pseudomonotonicity
  • Approximate solutions
  • Equilibrium problem
  • Navier-Stokes operator

Mathematics Subject Classification (2010)

  • 49J53
  • 49J40
  • 47H05
  • 47J20