SBD中的密度与断裂能的近似

IF 0.6 4区数学 Q3 MATHEMATICS

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2019-09-02 DOI:10.4171/rlm/859

V. Crismale

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引用次数: 3

摘要

在强BD拓扑中，我们证明了SBD函数的三个子空间的三个密度定理：SBD；SBD p∞，其中对称梯度的绝对连续部分在Lp中，其中p>1；SBD p，其函数在SBD p∞中，并且跳跃集具有有限的Hn−1-测度。我们将它们与现有的结果进行了比较，讨论了断裂能的相关近似。

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Density in SBD and approximation of fracture energies

. We prove three density theorems, in the strong BD topology, for the three subspaces of SBD functions: SBD ; SBD p ∞ , where the absolutely continuous part of the symmetric gradient is in L p , with p > 1 ; SBD p , whose functions are in SBD p ∞ and the jump set has ﬁ-nite H n − 1 -measure. We compare them with existing results, discussing related approximation of fracture energies.

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来源期刊

Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.