On the best constant in fractional $p$-Poincaré inequalities on cylindrical domains

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-03-31 DOI:10.57262/die034-1112-691

Kaushik Mohanta, Firoj Sk

引用次数: 7

Abstract

We investigate the best constants for the regional fractional $p$-Poincar\'e inequality and the fractional $p$-Poincar\'e inequality in cylindrical domains. For the special case $p=2$, the result was already known due to Chowdhury-Csat\'{o}-Roy-Sk [Study of fractional Poincar\'{e} inequalities on unbounded domains, Discrete Contin. Dyn. Syst., 41(6), 2021]. We addressed the asymptotic behaviour of the first eigenvalue of the nonlocal Dirichlet $p$-Laplacian eigenvalue problem when the domain is becoming unbounded in several directions.

查看原文本刊更多论文

圆柱域上分式$p$-Poincaré不等式的最佳常数

研究了区域分数阶$p$-Poincar\'e不等式和分数阶$p$-Poincar\'e不等式在圆柱形域上的最佳常数。对于特殊情况$p=2$，由于Chowdhury-Csat\ {o}-Roy-Sk[无界域上分数阶Poincar\ {e}不等式的研究，离散连续]，结果已经已知。直流发电机系统。农业科学，41(6)，2021 [j]。研究了当定义域在若干方向上无界时，非局部Dirichlet $p$- laplace特征值问题的第一个特征值的渐近行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.