ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - October 2007 - Volume 13, Issue 04  

Research Article

Γ-convergence of functionals on divergence-free fields

Ansini, Nadiaa1 and Garroni, Adrianaa2

a1 Section de Mathématiques, EPFL, 1015 Lausanne, Switzerland; nadia.ansini@epfl.ch

a2 Dip. di Matematica, Univ. di Roma `La Sapienza', P.le A. Moro 2, 00185 Rome, Italy; garroni@mat.uniroma1.it

Abstract

We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of Γ-convergence. We prove that the Γ-limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the Γ-limit is also stable under volume constraint and various type of boundary conditions.

(Received January 18 2006)

(Online publication September 5 2007)

Key Words:

  • ${\cal A}$ -quasiconvexity;
  • divergence-free fields;
  • Γ-convergence;
  • homogenization

Mathematics Subject Classification:

  • 35E99;
  • 35J99;
  • 49J45