Homogenization of variational problems in manifold valued BV-spaces

Abstract

This paper extends the result of Babadjian and Millot (preprint, 2008) on the homogenization of integral functionals with linear growth defined for Sobolev maps taking values in a given manifold. Through a Γ-convergence analysis, we identify the homogenized energy in the space of functions of bounded variation. It turns out to be finite for BV-maps with values in the manifold. The bulk and Cantor parts of the energy involve the tangential homogenized density introduced in Babadjian and Millot (preprint, 2008), while the jump part involves an homogenized surface density given by a geodesic type problem on the manifold.