Set-Valued and Variational Analysis

, Volume 22, Issue 4, pp 763–781 | Cite as

On the Boundedness of Solutions to Elliptic Variational Inequalities

  • Patrick Winkert


In this paper we present global a priori bounds for a class of variational inequalities involving general elliptic operators of second-order and terms of generalized directional derivatives. Based on Moser’s and De Giorgi’s iteration technique we prove the boundedness of solutions of such inequalities under certain criteria on the set of constraints. In our proofs we also use the localization method with a certain partition of unity and a version of a multiplicative inequality estimating the boundary integrals. Some sets of constraints satisfying the required conditions are stated as well.


A priori bounds Clarke’s gradient De Giorgi iteration Generalized directional derivative Moser iteration Variational-hemivariational inequality 

Mathematics Subject Classifications (2010)

35B45 35J25 35J60 35J87 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Technische Universität Berlin, Institut für MathematikBerlinGermany

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