Corpus ID: 220936507

Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2

@article{Antonelli2020DistributionalSO,
  title={Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2},
  author={Gioacchino Antonelli and Daniela Di Donato and Sebastiano Don},
  journal={arXiv: Metric Geometry},
  year={2020}
}
We prove that in arbitrary Carnot groups $\mathbb G$ of step 2, with a splitting $\mathbb G=\mathbb W\cdot\mathbb L$ with $\mathbb L$ one-dimensional, the graph of a continuous function $\varphi\colon U\subseteq \mathbb W\to \mathbb L$ is $C^1_{\mathrm{H}}$-regular precisely when $\varphi$ satisfies, in the distributional sense, a Burgers' type system $D^{\varphi}\varphi=\omega$, with a continuous $\omega$. We stress that this equivalence does not hold already in the easiest step-3 Carnot group… Expand
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