Work

Transport and flow for horizontal Sobolev contact velocities in Carnot groups

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.08738

Authors: Somma, Gianluca, Verzellesi, Simone, Vittone, Davide

Institution: Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7212083542

Cites: 1

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Related to: 10