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^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

58 Citations (Scopus)

Abstract

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].

Original language	English
Pages (from-to)	401-432
Number of pages	32
Journal	Archive for Rational Mechanics and Analysis
Volume	197
Issue number	2
DOIs	https://doi.org/10.1007/s00205-009-0269-y
Publication status	Published - 2010
Externally published	Yes

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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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",

issn = "0003-9527",

publisher = "Springer New York",

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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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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

Abstract

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