Minimizers of Caffarelli-Kohn-Nirenberg Inequalities with the singularity on the boundary

Jann Long Chern; Chang Shou Lin

doi:10.1007/s00205-009-0269-y

Minimizers of Caffarelli-Kohn-Nirenberg Inequalities with the singularity on the boundary

Jann Long Chern
, Chang Shou Lin^*

^*此作品的通信作者

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

58 引文斯高帕斯（Scopus）

摘要

Let Ω be a bounded smooth domain in R^N, N ≧ 3 and D_a^1,2(Ω) be the completion of C₀^∞(Ω) with respect to the norm, The Caffarelli-Kohn-Nirenberg inequalities state that there is a constant C > 0 such that, We prove the best constant for (0.1), is always achieved in D_a^1,2(Ω)} provided that 0 ∈ ∂Ω and the mean curvature H(0) < 0, where a, b satisfies If a = 0 and 1 > b > 0, then the result was proved by Ghoussoub and Robert [12].

原文	英語
頁（從 - 到）	401-432
頁數	32
期刊	Archive for Rational Mechanics and Analysis
卷	197
發行號	2
DOIs	https://doi.org/10.1007/s00205-009-0269-y
出版狀態	已發佈 - 2010
對外發佈	是

ASJC Scopus subject areas

分析
數學（雜項）
機械工業

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10.1007/s00205-009-0269-y

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title = "Minimizers of Caffarelli-Kohn-Nirenberg Inequalities with the singularity on the boundary",

abstract = "Let Ω be a bounded smooth domain in RN, N ≧ 3 and Da1,2(Ω) be the completion of C0∞(Ω) with respect to the norm, The Caffarelli-Kohn-Nirenberg inequalities state that there is a constant C > 0 such that, We prove the best constant for (0.1), is always achieved in Da1,2(Ω)\} provided that 0 ∈ ∂Ω and the mean curvature H(0) < 0, where a, b satisfies If a = 0 and 1 > b > 0, then the result was proved by Ghoussoub and Robert [12].",

author = "Chern, \{Jann Long\} and Lin, \{Chang Shou\}",

note = "Funding Information: Work partially supported by the National Science Council of Taiwan.",

year = "2010",

doi = "10.1007/s00205-009-0269-y",

language = "English",

volume = "197",

pages = "401--432",

journal = "Archive for Rational Mechanics and Analysis",

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T1 - Minimizers of Caffarelli-Kohn-Nirenberg Inequalities with the singularity on the boundary

AU - Chern, Jann Long

AU - Lin, Chang Shou

N1 - Funding Information: Work partially supported by the National Science Council of Taiwan.

PY - 2010

Y1 - 2010

N2 - Let Ω be a bounded smooth domain in RN, N ≧ 3 and Da1,2(Ω) be the completion of C0∞(Ω) with respect to the norm, The Caffarelli-Kohn-Nirenberg inequalities state that there is a constant C > 0 such that, We prove the best constant for (0.1), is always achieved in Da1,2(Ω)} provided that 0 ∈ ∂Ω and the mean curvature H(0) < 0, where a, b satisfies If a = 0 and 1 > b > 0, then the result was proved by Ghoussoub and Robert [12].

AB - Let Ω be a bounded smooth domain in RN, N ≧ 3 and Da1,2(Ω) be the completion of C0∞(Ω) with respect to the norm, The Caffarelli-Kohn-Nirenberg inequalities state that there is a constant C > 0 such that, We prove the best constant for (0.1), is always achieved in Da1,2(Ω)} provided that 0 ∈ ∂Ω and the mean curvature H(0) < 0, where a, b satisfies If a = 0 and 1 > b > 0, then the result was proved by Ghoussoub and Robert [12].

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DO - 10.1007/s00205-009-0269-y

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VL - 197

SP - 401

EP - 432

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 2

ER -

Minimizers of Caffarelli-Kohn-Nirenberg Inequalities with the singularity on the boundary

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