
\begin{center}

{\bf Higher Order Variational Problems and Equilibria and Relaxation in
Micromagnetics}

\vspace{.15in} 

Irene Fonseca
\end{center}

\vspace{.15in}

\noindent {\bf ABSTRACT}:Higher order variational theories are relevant in the study of
elasto-plastic materials (with micro cracks) and image segmentation in
computer vision (the Blake Zisserman model). Although several issues
involving lowersemicontinuity and relaxation can be recasted under the
notion of A-quasiconvexity, there are still many questions for variational
problems with higher derivatives that,  being completely understood in the
case of first order gradients, still defy the analysts. In order to
illustrate some of the difficulties encountered, in the first lecture we
will address lower semicontinuity (jointly with Giovanni Leoni and Jan
Maly) and phase transitions (jointly with Sergio Conti and Giovanni Leoni)
for multiple integrals involving second order derivatives.

The second lecture will be devoted to the study of exact minima of the
energy for large magnetic bodies with vanishing induced magnetic field
(with Bernard Dacorogna), followed by the characterization of the integral
representation of the relaxed energy in the absence of exchange energy (in
collaboration with Giovanni Leoni).

\vspace{.25in} 

\noindent Irene Fonseca\\
Carnegie Mellon University \\
Department of Mathematical Sciences \\
Pittsburgh, PA 15213 \\
email: fonseca@andrew.cmu.edu 

\end{document} 
\end


