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Journal of Applied Mathematics
Volume 2003 (2003), Issue 10, Pages 535-551

On the minimization of some nonconvex double obstacle problems

Fachbereich 6.1-Mathematik, Universität des Saarlandes, Postfach 15 11 50, Saarbrücken 66041, Germany

Received 11 October 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a nonconvex variational problem for which the set of admissible functions consists of all Lipschitz functions located between two fixed obstacles. It turns out that the value of the minimization problem at hand is equal to zero when the obstacles do not touch each other; otherwise, it might be positive. The results are obtained through the construction of suitable minimizing sequences. Interpolating these minimizing sequences in some discrete space, a numerical analysis is then carried out.