Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-08-04 DOI:10.4171/ifb/452

Maria Colombo, L. Spolaor, B. Velichkov

引用次数: 1

Abstract

We answer a question left open in [Arch. Rat. Mech. Anal. 230 (1) (2018), 125-184] and [Arch. Rat. Mech. Anal. 230 (2) (2018), 783-784], by proving that the blow-up limit of minimizers $u$ of the lower dimensional obstacle problem is unique at generic point of the free-boundary. Moreover we show that at such points the only admissible frequencies are $2m-1+s$ and $2m$, $m\geq 1$.

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对于低维障碍问题，几乎处处存在爆破极限的唯一性

我们回答了一个悬而未决的问题。老鼠。械甲怪。[j] .中国农业科学，2018，(1)，125-184。老鼠。械甲怪。[a] . 230(2)(2018)， 783-784]，通过证明低维障碍问题的最小化器的爆破极限$u$在自由边界的一般点上是唯一的。此外，我们表明，在这些点上，唯一允许的频率是$2m-1+s$和$2m$, $m\geq 1$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

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.