A trace theorem for spherical kinetic Sobolev spaces on $\rho$-convex domains

Herbert Egger; Matthias Schlottbom

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arXiv · 2608.19027

A trace theorem for spherical kinetic Sobolev spaces on $\rho$-convex domains

Herbert Egger·Matthias Schlottbom

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Abstract

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 $\rho$-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.

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Herbert Egger, Matthias Schlottbom. 2026-08-19. A trace theorem for spherical kinetic Sobolev spaces on $\rho$-convex domains. https://arxiv.org/abs/2608.19027

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