# American Institute of Mathematical Sciences

November  2013, 33(11&12): 4875-4890. doi: 10.3934/dcds.2013.33.4875

## On the asymptotic behavior of variational inequalities set in cylinders

 1 Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich 2 Technische Universität Darmstadt, Department of Mathematics, Schlossgartenstr. 7, D-64289 Darmstadt, Germany

Received  September 2011 Revised  March 2012 Published  May 2013

We study the asymptotic behavior of solutions to variational inequalities with pointwise constraint on the value and gradient of the functions as the domain becomes unbounded. First, as a model problem, we consider the case when the constraint is only on the value of the functions. Then we consider the more general case of constraint also on the gradient. At the end we consider the case when there is no force term which corresponds to Saint-Venant principle for linear problems.
Citation: Michel Chipot, Karen Yeressian. On the asymptotic behavior of variational inequalities set in cylinders. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 4875-4890. doi: 10.3934/dcds.2013.33.4875
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