双障碍问题固定边界附近自由边界的性质

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-10-20 DOI:10.1142/s1664360721500090

Jinwan Park

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引用次数: 2

摘要

本文研究了拉普拉斯算子和全非线性算子的双障碍问题的切向接触和固定边界附近自由边界的正则性。具有属性的主要思想是将上部障碍视为单个障碍问题的解决方案。那么，在对偶问题全局解的分类中，只考虑上障碍的两种情况就足够了，[公式:见文]第二种情况是一种新的上障碍，它在对偶问题自由边界局部正则性的研究中不存在。因此，本文主要研究来自第二类上障碍的一种新型困难。

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Properties of the free boundary near the fixed boundary of the double obstacle problems

In this paper, we study the tangential touch and [Formula: see text] regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator. The main idea to have the properties is regarding the upper obstacle as a solution of the single obstacle problem. Then, in the classification of global solutions of the double problem, it is enough to consider only two cases for the upper obstacle, [Formula: see text] The second one is a new type of upper obstacle, which does not exist in the study of local regularity of the free boundary of the double problem. Thus, in this paper, a new type of difficulties that come from the second type upper obstacle is mainly studied.

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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.