AI 中文总结
针对一般可具有非光滑边界的ρ-凸域，该研究建立球形动力学索伯列夫空间的新迹估计，利用特征线得到带显式常数的加权迹空间估计，并补充给出利普希茨域上对应函数空间的稠密性结果。
AI 中文摘要
迹定理是动力学方程分析的不可或缺工具，Cessenat及其合作者已针对辐射输运及相关应用建立了广泛适用的迹定理。针对动力学福克-普朗克方程和柯尔莫哥洛夫方程，已建立多种迹估计，通常要求基础域具有光滑性，参见Niebel与Valentini的最新综述。本研究中，我们针对ρ-凸域上的球形动力学索伯列夫空间证明了一项新的迹估计，该类域一般可具有非光滑边界。与Cessenat的工作类似，我们利用特征线在带显式常数的加权迹空间中获得迹估计；为完整性起见，我们还给出了利普希茨域上对应函数空间的稠密性结果。
英文摘要
Trace theorems are an indispensable tool for the analysis of kinetic equations. They have been established in wide generality by Cessenat and co-workers for radiative transfer and related applications. A variety of trace estimates have been established for the kinetic Fokker-Planck and Kolmogorov equation, typically requiring smoothness of the underlying domain; see the recent survey by Niebel \& Valentini. In this work, we prove a new trace estimate for kinetic Sobolev spaces over the sphere for $ρ$-convex domains which, in general, may have a non-smooth boundary. Similar to the work of Cessenat, we use characteristics to obtain trace estimates in weighted trace spaces with explicit constants. For completeness, we also present a density result for the corresponding function spaces on Lipschitz domains.
