TY - JOUR
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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U2 - 10.1007/s00205-009-0269-y
DO - 10.1007/s00205-009-0269-y
M3 - Article
AN - SCOPUS:77954174895
SN - 0003-9527
VL - 197
SP - 401
EP - 432
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -