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 A. Elfanni. 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.