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PreprintCC BY 4.0arXiv

Transport and flow for horizontal Sobolev contact velocities in Carnot groups

  • Gianluca Somma
  • Simone Verzellesi
  • Davide Vittone
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Abstract

We establish new well-posedness results for transport and flow equations driven by contact vector fields on Carnot groups. The velocity fields are assumed to have horizontal Sobolev regularity, namely Sobolev regularity only along the horizontal directions determined by the stratified geometry of the group. In the broader sub-Riemannian setting, results of this type were previously known only for Heisenberg groups. Our proof relies on the theory of renormalized solutions as originally introduced by DiPerna and Lions in the Euclidean setting.

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Cite

BibTeXRIS
BibTeX
@misc{somma2026transport,
  title = {{Transport and flow for horizontal Sobolev contact velocities in Carnot groups}},
  author = {Gianluca Somma and Simone Verzellesi and Davide Vittone},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08738},
  eprint = {2609.08738},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08738},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Transport and flow for horizontal Sobolev contact velocities in Carnot groups
AU  - Gianluca Somma
AU  - Simone Verzellesi
AU  - Davide Vittone
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08738
UR  - https://arxiv.org/abs/2609.08738
AB  - We establish new well-posedness results for transport and flow equations driven by contact vector fields on Carnot groups. The velocity fields are assumed to have horizontal Sobolev regularity, namely Sobolev regularity only along the horizontal directions determined by the stratified geometry of the group. In the broader sub-Riemannian setting, results of this type were previously known only for Heisenberg groups. Our proof relies on the theory of renormalized solutions as originally introduced by DiPerna and Lions in the Euclidean setting.
ER  -