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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.


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