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.
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页数：25
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