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arXiv · 2112.09485

Anisotropic Besov regularity of parabolic PDEs

Stephan Dahlke·Cornelia Schneider
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Abstract

This paper is concerned with the regularity of solutions to parabolic evolution equations. Special attention is paid to the smoothness in the specific anisotropic scale $\ B^{r\mathbf{a}}_{\tau,\tau}, \ \frac{1}{\tau}=\frac{r}{d}+\frac{1}{p}\ $ of Besov spaces where $\mathbf{a}$ measures the anisotropy. The regularity in these spaces determines the approximation order that can be achieved by fully space-time adaptive approximation schemes. In particular, we show that for the heat equation our results significantly improve previous results by Aimar and Gomez [3].

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Stephan Dahlke, Cornelia Schneider. 2021-12-17. Anisotropic Besov regularity of parabolic PDEs. https://arxiv.org/abs/2112.09485

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