On the Caffarelli-Kohn-Nirenberg inequalities: Sharp constants, existence (and nonexistence), and symmetry of extremal functions †

By Florin Catrina, Zhi-Qiang Wang. 2001

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Some improved Caffarelli-Kohn-Nirenberg inequalities (2005, methodology): “ii) By using a change of variables that appear in [ 8 ], Wang-Willem in [16] obtain the optimal reminder term related to (2) for the Caffarelli-Kohn-Nirenberg inequalities, �”
Existence and non-existence of solutions to elliptic equations related to the Caffarelli–Kohn–Nirenberg inequalities (2007, background): “In [12], the best constant Sα,β, the extremal functions and their quantitative properties were investigated again for p = 2.”
Minimizers of Caffarelli–Kohn–Nirenberg Inequalities with the Singularity on the Boundary (2010, background): “4) have been extensively studied for the past 20 years, see [5,6,13,17,20] and references therein.”
Partial symmetry and asymptotic behavior for some elliptic variational problems (2003, background): “ Theorem (Catrina and Wang [ 10 ]).”
Singular elliptic problems with lack of compactness (2005, background): “We point out that the inequality (4) also holds true for b = a + 1 (if N ≥ 1) and b = a (if N ≥ 3) but, in these cases, the best Sobolev constant Ca,b in (4) is never achieved (see [7] for details).”
A global compactness result for singular elliptic problems involving critical Sobolev exponent (2002, neutral): “problem (see [4], [10], [12] and [14]) (1.”