Improved fractional Trudinger-Moser inequalities on bounded intervals and the existence of their extremals

Lu Chen; Bohan Wang; Maochun Zhu

doi:10.1515/ans-2022-0067

Improved fractional Trudinger-Moser inequalities on bounded intervals and the existence of their extremals

Lu Chen, Bohan Wang, Maochun Zhu^*

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

13 引用（Scopus）

摘要

Let I be a bounded interval of ℝ and λ1(I) denote the first eigenvalue of the nonlocal operator (-Δ)1/4 with the Dirichlet boundary. We prove that for any 0 ≤ α < λ1(I), there holds (Equation Presented) and the supremum can be attained. The method is based on concentration-compactness principle for fractional Trudinger-Moser inequality, blow-up analysis for fractional elliptic equation with the critical exponential growth and harmonic extensions.

源语言	英语
文章编号	20220067
期刊	Advanced Nonlinear Studies
卷	23
期	1
DOI	https://doi.org/10.1515/ans-2022-0067
出版状态	已出版 - 1 1月 2023

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Chen, L., Wang, B., & Zhu, M. (2023). Improved fractional Trudinger-Moser inequalities on bounded intervals and the existence of their extremals. Advanced Nonlinear Studies, 23(1), 文章 20220067. https://doi.org/10.1515/ans-2022-0067

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abstract = "Let I be a bounded interval of ℝ and λ1(I) denote the first eigenvalue of the nonlocal operator (-Δ)1/4 with the Dirichlet boundary. We prove that for any 0 ≤ α < λ1(I), there holds (Equation Presented) and the supremum can be attained. The method is based on concentration-compactness principle for fractional Trudinger-Moser inequality, blow-up analysis for fractional elliptic equation with the critical exponential growth and harmonic extensions.",

keywords = "Trudinger-Moser inequalities, extremals, fractional",

author = "Lu Chen and Bohan Wang and Maochun Zhu",

note = "Publisher Copyright: {\textcopyright} 2023 the author(s), published by De Gruyter.",

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doi = "10.1515/ans-2022-0067",

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T1 - Improved fractional Trudinger-Moser inequalities on bounded intervals and the existence of their extremals

AU - Chen, Lu

AU - Wang, Bohan

AU - Zhu, Maochun

PY - 2023/1/1

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N2 - Let I be a bounded interval of ℝ and λ1(I) denote the first eigenvalue of the nonlocal operator (-Δ)1/4 with the Dirichlet boundary. We prove that for any 0 ≤ α < λ1(I), there holds (Equation Presented) and the supremum can be attained. The method is based on concentration-compactness principle for fractional Trudinger-Moser inequality, blow-up analysis for fractional elliptic equation with the critical exponential growth and harmonic extensions.

AB - Let I be a bounded interval of ℝ and λ1(I) denote the first eigenvalue of the nonlocal operator (-Δ)1/4 with the Dirichlet boundary. We prove that for any 0 ≤ α < λ1(I), there holds (Equation Presented) and the supremum can be attained. The method is based on concentration-compactness principle for fractional Trudinger-Moser inequality, blow-up analysis for fractional elliptic equation with the critical exponential growth and harmonic extensions.

KW - Trudinger-Moser inequalities

KW - extremals

KW - fractional

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JO - Advanced Nonlinear Studies

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Improved fractional Trudinger-Moser inequalities on bounded intervals and the existence of their extremals

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