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

2013/07/16 by Andrea Pinamonti, Francesco Serra Cassano, Giulia Treu +1 · 1 citation
Mathematics · #math.MG #math.AP

paper · pdf · doi:10.2422/2036-2145.201305_004

arxiv created 2013/07/16 · arxiv updated 2013/10/29

Abstract

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

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