Calculus of Variations and Geometric Measure Theory
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A. Pinamonti - F. Serra Cassano - G. Treu - D. Vittone

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

created by pinamonti on 27 Mar 2013
modified by vittone on 25 Jul 2017


Published Paper

Inserted: 27 mar 2013
Last Updated: 25 jul 2017

Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
Volume: 14
Number: 3
Pages: 907--935
Year: 2015
Doi: 10.2422/2036-2145.201305_004


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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