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We consider the area functional for t-graphs in the sub-Riemannian Heisenberggroup and study minimizers of the associated Dirichlet problem. We prove that,under a bounded slope condition on the boundary datum, there exists a uniqueminimizer and that this minimizer is Lipschitz continuous. We also provide anexample showing that, in the first Heisenberg group, Lipschitz regularity issharp even under the bounded slope condition.

BV Minimizers of the area functional in the Heisenberg group under the bounded slope condition