Calculus of Variations and Geometric Measure Theory
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G. Antonelli - A. Merlo

Intrinsically Lipschitz functions with normal targets in Carnot groups

created by antonelli on 05 Jun 2020
modified on 04 Aug 2020

[BibTeX]

Submitted Paper

Inserted: 5 jun 2020
Last Updated: 4 aug 2020

Year: 2020

ArXiv: 2006.02782 PDF

Abstract:

We provide a Rademacher theorem for intrinsically Lipschitz functions $\phi:U\subseteq \mathbb W\to \mathbb L$, where $U$ is a Borel set, $\mathbb W$ and $\mathbb L$ are complementary subgroups of a Carnot group, where we require that $\mathbb W$ is a Carnot subgroup and $\mathbb L$ is a normal subgroup. Our hypotheses are satisfied for example when $\mathbb W$ is a horizontal subgroup. Moreover, we provide an area formula for this class of intrinsically Lipschitz functions.

Tags: GeoMeG

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