Minimizers of Caffarelli-Kohn-Nirenberg Inequalities with the Singularity on the Boundary

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/51136

Title:	Minimizers of Caffarelli-Kohn-Nirenberg Inequalities with the Singularity on the Boundary
Authors:	Chern,JL;Lin,CS
Contributors:	數學系
Keywords:	SEMILINEAR ELLIPTIC-EQUATIONS;INTERPOLATION INEQUALITIES;EXTREMAL-FUNCTIONS;POSITIVE SOLUTIONS;SCALAR CURVATURE;SHARP CONSTANTS;SOBOLEV;SYMMETRY;NONEXISTENCE;EXISTENCE
Date:	2010
Issue Date:	2012-03-27 18:22:56 (UTC+8)
Publisher:	國立中央大學
Abstract:	Let Omega be a bounded smooth domain in R(N), N >= 3, and D(a)(1,2) (Omega) be the completion of C(0)(infinity) (Omega) with respect to the norm: \|\|u\|\|(2)(a) = integral(Omega)\|x\|(-2a)\|del u\|(2)dx. The Caffarelli-Kohn-Nirenberg inequalities state that there is a constant C > 0 such that (integral(Omega)\|x\|(-bq)\|u\|(q)dx)(2/q) <= C integral(Omega)\|x\|(-2a)\|del u\|dx for u is an element of D(a)(1,2) (Omega) and [GRAPHICS] We prove the best constant for (0.1) [GRAPHICS] is always achieved in D(a)(1,2) (Omega) provided that 0 is an element of partial derivative Omega and the mean curvature H(0) < 0, where a, b satisfies (i) a < b < a + 1 and N >= 3, or (ii) b = a > 0 and N >= 4. If a = 0 and 1 > b > 0, then the result was proved by Ghoussoub and Robert [12].
Relation:	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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