Directional differentiability for elliptic quasi-variational inequalities of obstacle type

  • Amal Alphonse
  • Michael Hintermüller
  • Carlos N. RautenbergEmail author


The directional differentiability of the solution map of obstacle type quasi-variational inequalities (QVIs) with respect to perturbations on the forcing term is studied. The classical result of Mignot is then extended to the quasi-variational case under assumptions that allow multiple solutions of the QVI. The proof involves selection procedures for the solution set and represents the directional derivative as the limit of a monotonic sequence of directional derivatives associated to specific variational inequalities. Additionally, estimates on the coincidence set and several simplifications under higher regularity are studied. The theory is illustrated by a detailed study of an application to thermoforming comprising of modelling, analysis and some numerical experiments.

Mathematics Subject Classification

47J20 49J40 49J52 49J50 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Amal Alphonse
    • 1
  • Michael Hintermüller
    • 1
  • Carlos N. Rautenberg
    • 1
    Email author
  1. 1.Weierstrass InstituteBerlinGermany

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