Characterization of the variable exponent Sobolev norm without derivatives

被引：6

作者：

Hasto, Peter ^{[1
,2
]}

Ribeiro, Ana Margarida ^{[3
,4
]}

机构：

[1] Univ Oulu, Dept Math Sci, POB 3000, FI-90014 Oulu, Finland

[2] Univ Turku, Dept Math & Stat, Turku, Finland

[3] Univ Nova Lisboa, Fac Ciencias & Tecnol, CMA, P-2829516 Caparica, Portugal

[4] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, P-2829516 Caparica, Portugal

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2017年 / 19卷 / 03期

关键词：

Non-standard growth; variable exponent; Sobolev space; Gagliardo seminorm; SPACES; FUNCTIONALS; SMOOTHNESS;

D O I：

10.1142/S021919971650022X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Since the difference quotient is based on shifting the function, it cannot be generalized to the variable exponent case. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the variable exponent Sobolev space.

引用

页数：13

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