Set-Valued and Variational Analysis

, Volume 26, Issue 3, pp 631–642 | Cite as

On the Directional Differentiability of the Solution Mapping for a Class of Variational Inequalities of the Second Kind

  • M. HintermüllerEmail author
  • T. M. Surowiec


The directional differentiability of the solution mapping for a class of variational inequalities of the second kind inspired by applications in fluid mechanics and moving free boundary problems is investigated. The result is particularly relevant for the model predictive control or optimal control of such variational inequalities in that it can be used to derive stationarity conditions and efficient numerical methods.


Variational inequalities of the second kind Free boundary problems Variational analysis Generalized differentiation Hadamard directional differentiability Conical differentiability Control-to-state mapping Optimal control of variational inequalities PDE-constrained optimization 

Mathematics Subject Classifications (2010)

35B30 35B37 35J88 35R35 49A29 49J20 49K20 49J40 49J53 47J20 93C20 


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The authors would like to thank C. Christof and C. Meyer for pointing out a potential inconsistency in the original manuscript and for making us aware of the work [4].


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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of MathematicsHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Department of Mathematics and Computer SciencePhilipps-Universität MarburgMarburgGermany
  3. 3.Weierstrass InstituteBerlinGermany

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