Calculus of Variations and Geometric Measure Theory

G. Buttazzo - C. Timofte

On The Relaxation of Some Optimal Partition Problems

created on 12 Sep 2001
modified on 19 Sep 2001



Inserted: 12 sep 2001
Last Updated: 19 sep 2001

Pages: 11
Year: 2001


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\begin{document} We consider optimization problems for which the cost functional depends on a partition of a given domain $\Omega .$ It is well known that, unless we assume special monotonicity conditions on the cost functional or geometric constraints on the class of admissible choices, an optimal solution does not exist and a relaxation procedure is then necessary to describe the asymptotic behavior of the minimizing sequences. In this paper we determine the form of the relaxed optimization problem. \end{document}