%last revised December 10, 1998
\input amstex
\documentstyle{amsppt}
%\magnification=\magstep1
\pagewidth{16.4truecm}
\pageheight{22truecm}
\NoBlackBoxes
\language09
\nologo
\TagsOnRight
\def\loc{_{\operatorname{loc}}}
\def\avint{ \int\!\!\!\!\!\!-}


\topmatter \title On lower semicontinuity\\and relaxation\endtitle
\author Irene Fonseca\,\dag\quad\&\quad Giovanni
Leoni\,\ddag\endauthor \abstract Lower semicontinuity and relaxation
results in BV are obtained for multiple integrals
$$
F(u,\Omega):=\int_\Omega f(x,u(x),\nabla u(x))\,dx, \quad u \in W^{1,1}(\Omega;\Bbb R^d),
$$
where the energy density $f$ satisfies lower semicontinuity conditions with respect to $(x,u)$ and is not subjected to coercivity hypotheses. These results call for methods recently developed in the Calculus of Variations.                 
\endabstract



\subjclass 49J45,  49Q20\endsubjclass

\keywords Functions of bounded variation, lower semicontinuity,
relaxation, convexity, quasiconvexity\endkeywords



\endtopmatter
\leftheadtext\nofrills{I. Fonseca and G. Leoni}
\rightheadtext\nofrills{Lower semicontinuity and relaxation}
\document
\footnote""{\dag\quad Department of Mathematical Sciences, Carnegie Mellon
University, Pittsburgh, PA 15213}
\footnote""{\ddag\quad   Dipartimento di Scienze e Tecnologie
Avanzate, Universit\'a del Piemonte Orientale, Alessandria, Italy 15100.}

