This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations extending our findings in Dahlke and Schneider (Anal Appl 17(2):235–291, 2019, Thms. 4.5, 4.9, 4.12, 4.14) to domains of polyhedral type. In particular, we study the smoothness in the specific scale \(\ B^r_{\tau ,\tau }, \ \frac{1}{\tau }=\frac{r}{d}+\frac{1}{p}\ \) of Besov spaces. The regularity in these spaces determines the approximation order that can be achieved by adaptive and other nonlinear approximation schemes. We show that for all cases under consideration the Besov regularity is high enough to justify the use of adaptive algorithms.

本文关注线性和非线性演化方程的解的规律性，将我们在 Dahlke 和 Schneider（Anal Appl 17(2):235–291, 2019, Thms. 4.5, 4.9, 4.12, 4.14）中的发现扩展到多面体域类型。特别地，我们研究了特定尺度\(\ B^r_{\tau ,\tau }, \ \frac{1}{\tau }=\frac{r}{d}+\frac{1} {p}\ \)的 Besov 空间。这些空间中的规律性决定了可以通过自适应和其他非线性逼近方案实现的逼近阶数。我们表明，对于所考虑的所有情况，Besov 正则性足以证明使用自适应算法是合理的。