Regularity in Sobolev and Besov spaces for parabolic problems on domains of polyhedral type

TL;DR

This paper investigates the regularity of solutions to linear and nonlinear parabolic equations on polyhedral domains within Besov spaces, demonstrating sufficient smoothness to support adaptive approximation methods.

Contribution

It extends previous regularity results to polyhedral domains and analyzes Besov space smoothness relevant for adaptive algorithms.

Findings

Besov regularity is high enough for adaptive algorithms.

Regularity results extend to nonlinear evolution equations.

Supports the use of nonlinear approximation schemes.

Abstract

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.