Homogenization of Variational Problems in Manifold Valued Bv -spaces

Abstract. This paper extends the result of [9] 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 [9], while the jump part involves an homogenized surface density given by a geodesic type problem on the manifold.