Differentiability properties of functions from higher-order Orlicz-Sobolev spaces

被引：3

作者：

Cianchi, Andrea ^{[1
]}

Randolfi, Monia ^{[2
]}

机构：

[1] Univ Firenze, Dipartimento Matemat U Dini, I-50122 Florence, Italy

[2] Univ Firenze, Dipartimento Matemat U Dini, I-50134 Florence, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 07期

关键词：

Orlicz-Sobolev spaces; Lebesgue points; Pointwise differentiability; Approximate differentiability; EXPONENTIAL INTEGRABILITY; GRADIENTS; EXTENSION;

D O I：

10.1016/j.na.2011.12.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze pointwise differentiability properties of functions from (local) Orlicz-Sobolev spaces W-loc(m,A)(Omega) on an open subset Omega of R-n, n >= 2. A necessary and sufficient condition on the order of differentiation m and on the Young function A is exhibited for any function in W-loc(m,A)(Omega) to admit a differential of order m a. e. in Omega. An optimal approximate differentiability property in integral and norm form is established when such a condition fails. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：3322 / 3338

页数：17

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