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On the stability constant of Caffarelli-Kohn-Nirenberg inequality
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abstract
By using a spectral analysis, we first show that the Caffarelli--Kohn--Nirenberg inequality with gradient remainder term of any order less than $4$ does not hold on the {\em Felli-Schneider} curve $b_{\mathrm{FS}}(a)$. Furthermore, we prove the existence of minimizers of sharp stability constant of Caffarelli--Kohn--Nirenberg inequality near the new curve $b^*_{\mathrm{FS}}(a)(>b_{\mathrm{FS}}(a))$, which extends the work of Wei and Wu [Math. Z., 2024] to a sightly larger region.
Forward citations
Cited by 2 Pith papers
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Stability inequalities with explicit constants for a family of reverse Sobolev inequalities on the sphere
The sharp stability constant for the reverse Sobolev inequality on S^n equals 1 for s-n/2 in (1,2) and is not attained, while the range (0,1) has a positive constant with explicit upper bound.
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Optimal Stability Bounds, Minimizers, and Critical Points for a Critical Nonlocal Sobolev Inequality on the Heisenberg Group
The paper claims optimal Bianchi-Egnell constants for a nonlocal Sobolev inequality on the Heisenberg group, but the key strict spectral bound is unproved.
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