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

DOI10.2422/2036-2145.201305_004zbMath1330.49044arXiv1307.4442OpenAlexW2962802522MaRDI QIDQ3460887

Davide Vittone, Andrea Pinamonti, Francesco Serra Cassano, Giulia Treu

Publication date: 8 January 2016

Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.4442

zbMATH Keywords

Lipschitz continuityarea functionalsub-Riemannian Heisenberg groupbounded slope conditionBV minimizers

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Variational problems in a geometric measure-theoretic setting (49Q20) Regularity of solutions in optimal control (49N60) Optimization of shapes other than minimal surfaces (49Q10) Sub-Riemannian geometry (53C17)

Related Items (9)

On the Lipschitz Regularity for Minima of Functionals Depending on $x$, $u$, and $\nabla{u}$ under the Bounded Slope Condition ⋮ Area-stationary and stable surfaces of class \(C^1\) in the sub-Riemannian Heisenberg group \(\mathbb{H}^1\) ⋮ Non-occurrence of the Lavrentiev phenomenon for a class of convex nonautonomous Lagrangians ⋮ Area-minimizing horizontal graphs with low regularity in the sub-Finsler Heisenberg group \({\mathbb{H}}^1\) ⋮ Uniqueness of generalized \(p\)-area minimizers and integrability of a horizontal normal in the Heisenberg group ⋮ Poincaré-type inequality for Lipschitz continuous vector fields ⋮ Lipschitz minimizers for a class of integral functionals under the bounded slope condition ⋮ Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient ⋮ Existence and structure of \(P\)-area minimizing surfaces in the Heisenberg group

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