Estimates for L1 vector fields under higher-order differential conditions

被引：0

作者：

Van Schaftingen, Jean ^{[1
]}

机构：

[1] Univ Catholique Louvain, Dept Math, B-1348 Louvain, Belgium

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2008年 / 10卷 / 04期

关键词：

Critical Sobolev spaces; compensation; Sobolev inequality; Korn-Sobolev inequality;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that an L(1) vector field whose components satisfy some condition on k-th order derivatives induce linear functionals on the Sobolev space W(1,n)(R(n)). Two proofs are provided, relying on the two distinct methods developed by Bourgain and Brezis (J. Eur. Math. Soc., 2007) and by the author (C. R. Math. Acad. Sci. Paris, 2004) to prove the same result for divergence-free vector fields and partial extensions to higher-order conditions.

引用

页码：867 / 882

页数：16

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