各向异性函数不存在拉夫连季耶夫缺口

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Michał Borowski, Iwona Chlebicka, Błażej Miasojedow
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引用次数: 0

摘要

我们证明了对于一般结构的非自治变分问题,在索波列夫映射和光滑映射之间不存在拉夫连季耶夫缺口,在该问题中,积分被假定由一个函数控制,而该函数相对于最后一个变量是凸的和各向异性的。这一事实源于关于自然底层非常规函数空间精细逼近特性的新结果。对标量和矢量值问题进行了研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Absence of Lavrentiev’s gap for anisotropic functionals

We establish the absence of the Lavrentiev gap between Sobolev and smooth maps for a non-autonomous variational problem of a general structure, where the integrand is assumed to be controlled by a function which is convex and anisotropic with respect to the last variable. This fact follows from new results on fine approximation properties of the natural underlying unconventional function space. Scalar and vector-valued problems are studied.

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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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