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-11

A Relaxation Theorem in the Space of Functions of Bounded Deformation

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

Ana Cristina Barroso
C.M.A.F.
Av. Prof. Gamma Pinto 2
1699 Lisboa Codex, Portugal
mail: abarroso@lmc.fc.ul.pt

Rodica Toader
C.M.A.F.
Av. Prof. Gamma Pinto 2
1699 Lisboa Codex, Portugal

Abstract: We obtain an integral representation for the relaxation, in the space of functions of bounded deformation, of the energy
\begin{displaymath}\int_{\Omega}f({\mathcal E}u(x))dx \end{displaymath}

with respect to L1-convergence. Here ${\mathcal E}u$ represents the absolutely continuous part of the symmetrized distributional derivative Eu and the function f satisfies linear growth and coercivity conditions.

Keywords : functions of bounded deformation, relaxation, E-quasiconvexity

1991 Mathematics Subject Classification: 35J50, 49J45, 49Q20, 73E99. 2000 Mathematics Subject Classification: 35J50, 49J45, 49Q20, 74C15, 74G65.


Get the paper in its entirety as

 

Back to CNA Publications