Sobolev space of functions valued in a monotone Banach family

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:492

Article

Evseev, Nikita¹  Menovschikov, Alexander² 

[1] Harbin Inst Technol, Inst Adv Study Math, Harbin 150001, Peoples R China

[2] Sobolev Inst Math, Novosibirsk 630090, Russia

关键词: Sobolev spaces of vector-valued functions;    L-p-direct integral;    Bochner integral;   

DOI  :  10.1016/j.jmaa.2020.124440

来源: Elsevier

【 摘 要 】

We apply the metrical approach to Sobolev spaces, which arise in various evolution PDEs. Functions from those spaces are defined on an interval and take values in a nested family of Banach spaces. In this case we adapt the definition of Newtonian spaces. For a monotone family, we show the existence of weak derivative, obtain an isomorphism to the standard Sobolev space, and provide some scalar characteristics. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free