圆柱域上分式$p$-Poincaré不等式的最佳常数

IF 1.8 4区数学 Q1 MATHEMATICS

Differential and Integral Equations Pub Date : 2021-03-31 DOI:10.57262/die034-1112-691

Kaushik Mohanta, Firoj Sk

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引用次数: 7

摘要

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。

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

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.

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来源期刊

Differential and Integral Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential and Integral Equations will publish carefully selected research papers on mathematical aspects of differential and integral equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new, and of interest to a substantial number of mathematicians working in these areas.