Sobolev space of functions valued in a monotone Banach family

被引：3

作者：

Evseev, Nikita ^{[1
]}

Menovschikov, Alexander ^{[2
]}

机构：

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

[2] Sobolev Inst Math, Novosibirsk 630090, Russia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 492卷 / 01期

关键词：

Sobolev spaces of vector-valued functions; L-p-direct integral; Bochner integral; PARABOLIC PDES; EQUATIONS;

D O I：

10.1016/j.jmaa.2020.124440

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页数：25

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