*Preprint*

**Inserted:** 12 sep 2001

**Last Updated:** 19 sep 2001

**Pages:** 11

**Year:** 2001

**Abstract:**

% Theorem environments %% \theoremstyle{plain} %% This is the default % to make the notation environment unnumbered %\newtheorem{theorem}{Theorem}section %\newtheorem{corollary}theorem{Corollary} %\newtheorem{lemma}theorem{Lemma} %\newtheorem{proposition}theorem{Proposition} %\newtheorem{axiom}{Axiom} %\newtheorem{definition}{Definition}section %\newtheorem{remark}{Remark}section %\newtheorem{notation}{Notation} %\renewcommand{\thenotation}{}

\documentclass{amsart} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{amscd} \usepackage{thmdefs}

%TCIDATA{TCIstyle=Article*art1.lat,amsart,amsart}
*

%TCIDATA{Created=Tue Sep 11 22:38:19 2001} %TCIDATA{LastRevised=Tue Sep 11 22:38:19 2001}

\input{tcilatex} \theoremstyle{definition} \theoremstyle{remark} \numberwithin{equation}{section} \newcommand{\thmref}1{Theorem \ref{#1}} \newcommand{\secref}1{\S\ref{#1}} \newcommand{\lemref}1{Lemma \ref{#1}}

\input tcilatex

*\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}
*

**Download:**