Regularity in Sobolev and Besov Spaces for Parabolic Problems on Domains of Polyhedral Type

作     者：Dahlke, Stephan Schneider, Cornelia 

作者机构：Philipps Univ Marburg FB12 Math & Comp Sci Hans Meerwein Str D-35032 Marburg Germany Friedrich Alexander Univ Erlangen Nuremberg Appl Math 3 Cauerstr 11 D-91058 Erlangen Germany 

出 版 物：《JOURNAL OF GEOMETRIC ANALYSIS》 (几何分析杂志)

年 卷 期：2021年第31卷第12期

页      面：11741-11779页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Deutsche Forschungsgemeinschaft (DFG) [SCHN 1509/1-2] 

主　　题：Parabolic evolution equations Besov spaces Kondratiev spaces Adaptive algorithms 

摘      要：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-tau,tau(r), 1/tau = r/d + 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.