CMU Campus
Center for                           Nonlinear Analysis
CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact
Publication 99-CNA-28

A-Quasiconvexity: Relaxation and Homogenization

Andrea Braides
S.I.S.S.A.
Trieste, Italy

and

Irene Fonseca
Department of Mathematical Sciences
Carnegie-Mellon University
Pittsburgh, PA, U.S.A.

and

Giovanni Leoni
Dipartimento di Scienze e Tecnologie Avanzate
Università del Piemonte Orientale
Alessandria, Italy


ABSTRACT: Integral representation of relaxed energies and of $\Gamma$-limits of functionals

\begin{displaymath}(u,v)\mapsto \int_\Omega f( x,u(x),v(x))\,dx \end{displaymath}

are obtained when sequences of fields v may develop oscillations and are constrained to satisfy a system of first order linear partial differential equations. This framework includes the treatement of divergence-free fields, Maxwell's equations in micromagnetics, and curl-free fields. In the latter case classical relaxation theorems in W1,p are recovered.

Get the paper in its entirety as