具有规定跳跃方向的有界变分函数的特殊函数的强逼近

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-12-19 DOI:10.1002/mana.202300346

Giuliano Lazzaroni, Piotr Wozniak, Caterina Ida Zeppieri

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引用次数: 0

摘要

在这篇文章中，我们证明了跳跃法线在指定方向N $\mathcal {N}$上的有界变差（SBV） $\ mathm {SBV)}$函数的特殊函数可以用跳跃集为的SBV $\ mathm {SBV}$函数序列来逼近本质上是封闭的多面体，并且保持了与N $\mathcal {N}$的正交性，并且函数平滑地远离了它们的跳跃集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Strong approximation of special functions of bounded variation functions with prescribed jump direction

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Strong approximation of special functions of bounded variation functions with prescribed jump direction

In this note, we show that special functions of bounded variation ( $SBV)$ functions with jump normal lying in a prescribed set of directions $N$ can be approximated by sequences of $SBV$ functions whose jump set is essentially closed, polyhedral, and preserves the orthogonality to $N$ , moreover the functions are smooth away from their jump set.

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index