Carnot群中水平Sobolev接触速度的输运与流
Transport and flow for horizontal Sobolev contact velocities in Carnot groups
- University of Padova（帕多瓦大学）
- Bocconi University（博科尼大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文在Carnot群上建立了由水平Sobolev接触速度场驱动的输运与流方程的适定性，推广了先前仅适用于Heisenberg群的结果，证明基于重正规化解理论。
中文摘要 AI 辅助
我们在Carnot群上建立了由接触向量场驱动的输运方程和流方程的新的适定性结果。速度场被假定具有水平Sobolev正则性，即仅沿由群的层状几何确定的水平方向具有Sobolev正则性。在更广泛的次黎曼背景下，此类结果此前仅对Heisenberg群已知。我们的证明依赖于DiPerna和Lions在欧几里得背景下最初引入的重正规化解理论。
英文摘要
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.
