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

Abstract

We consider functions $u:{\mathbb{R}}^2\to {\mathbb{R}}^N$ 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.