Relaxation Results for a Class of Functionals with Linear Growth Defined on Manifold Constrained Mappings

We study the lower semicontinuous envelope of a class of functionals with linear growth defined on mappings from the n-dimensional ball B ⁿ into

, that are constrained to take values into a smooth submanifold

\mathcal{Y} Y

of

\mathbb{R}^N R N