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arXiv · 2311.10838

The Mixed Convex-Concave effect on the regularity of a Boltzmann solution

Gayoung An·Donghyun Lee
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Abstract

The geometric properties of domains are well-known to be crucial factors influencing the regularity of Boltzmann boundary problems. In the presence of non-convex physical boundaries, highly singular behaviors are investigated including the propagation of discontinuities \cite{Kim11} and H\"older regularity \cite{CD2022}. In this paper, we focus on studying the $C^{0,\frac{1}{4}-}$ H\"older regularity of the Boltzmann equation within concentric cylinders where both convex and concave features are present on the boundaries. Our findings extend the previous results of \cite{CD2022}, which primarily addressed concavity while considering the exterior of convex objects.

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Gayoung An, Donghyun Lee. 2023-11-17. The Mixed Convex-Concave effect on the regularity of a Boltzmann solution. https://doi.org/10.1137/24m1670354

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