A geometric maximum principle for variational problems in spaces of vector valued functions of bounded variation

We discuss variational integrals with density having linear growth on spaces of vector valued $BV$-functions and prove $\operatorname{Im}(u)\subset K$ for minimizers $u$ provided that the boundary data take their values in the closed convex set $K$ assuming in addition that the integrand satisfies natural structure conditions. Bibl. 14 titles.