The Liouville property for entire local minimizers from the space $BV_{\mathrm{loc}}(\R^2,\R^N)$ of variational integrals with linear growth

We consider functions $u : \R^2 \rightarrow \R^N$ from the class $\Bloc$ which locally minimize the relaxed version of a variational integral with a strictly convex density being in addition of linear growth. It turns out that the boundedness of entire local minimizers $u$ implies their constancy.