Vector-valued Sobolev spaces based on Banach function spaces

被引：2

作者：

Evseev, Nikita ^{[1
,2
]}

机构：

[1] Harbin Inst Technol, Inst Adv Study Math, Harbin 150006, Peoples R China

[2] Russian Acad Sci, Steklov Math Inst, Moscow 119991, Russia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2021年 / 211卷

基金：

俄罗斯科学基金会;

关键词：

Sobolev spaces; Banach function space; Vector-valued functions; Reshetnyak-Sobolev space; Newtonian space;

D O I：

10.1016/j.na.2021.112479

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is known that there are several approaches to define a Sobolev class for Banach valued functions. We compare the usual definition via weak derivatives with the Reshetnyak-Sobolev space and with the Newtonian space; in particular, we provide sufficient conditions when all three agree. Also, we revise the difference quotient criterion and the property of Lipschitz mapping to preserve Sobolev space when it is acting as a superposition operator. (C) 2021 Elsevier Ltd. All rights reserved.

引用

页数：15

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