Anisotropic Besov regularity of parabolic PDEs

12/17/2021

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by   Stephan Dahlke, et al.

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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^r𝐚_τ,τ, 1/τ=r/d+1/p of Besov spaces where 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].