This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations extending our findings in [22] to domains of polyhedral type. In particular, we study the smoothness in the specific scale $B^r_{\tau,\tau}$, $\frac{1}{\tau}=\frac rd+\frac 1p$ 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.

翻译：本文关注线性和非线性进化方程式解决方案的规律性,这些方程式将我们在[22]中的调查结果扩大到多面型领域,特别是,我们研究了具体规模的平滑性($Bär ⁇ tau,\tau}$,$\frac{1untau ⁇ frac rd ⁇ frac 1p$)。这些空格的规律性决定了适应性和其他非线性近似计划所能达到的近似顺序。我们表明,在所审议的所有情况下,Besov的规律性都足以证明使用适应性算法是合理的。