Chow and Rashevskii meet Sobolev

Key Points

• Proving a weak version of the chow-rashevskii theorem broadens its applicability to sobolev regularity.
• Flows generated from sobolev regular vector fields lead to selections of ODE solutions for almost every initial datum.
• Findings indicate potential advancement in fields utilizing vector fields and their dynamics.
• Implications for various mathematical problems arise from integrating sobolev regularity with the chow-rashevskii theorem.