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=Articleart1.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}
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