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PDF | By methods based on elementary Linear Algebra we obtain sharp *constants* in *cases* of the Caffarelli-*Kohn*-Nirenberg *inequality* via quasi-conformal ...

https://www.researchgate.net/publication/312062017_investigate the symmetry and symmetry breaking of the optimizers of the CKN, in the case p D2 and t D1 using a nonlinear ﬂow approach. In the case t 6D1 and p D2, the best constants of the CKN inequality were investigated in[Dolbeault and Esteban 2012]. In addition toTheorem 1.2we prove a symmetry breaking phenomenon for the case >0: …

http://aurak.ac.ae/publications/In Appendix, we provide cross-references between the results of this paper and the results in for the case \(N=2\), one of them being representation of the Moser–Trudinger inequality as a two-dimensional case of the Sobolev embedding for the hyperbolic space.

https://link.springer.com/article/10.1007/s10231-017-0650-7In this paper, we present a version of horizontal weighted Hardy-Rellich type and Caffarelli-Kohn-Nirenberg type inequalities on stratified groups and study some of their …

https://www.researchgate.net/publication/302575994_Lp-Caffarelli...“boundary” of the a-negative region. SinceS.a;b/is continuous, we also ob-tain estimates for S.a;b/near the boundary of the parameter domain. From Theorems 1.2 and 1.3, there are no closed-form minimizers, so it seems to be very difﬁcult to examine the best constants in the interior of the region. 2.

http://www.math.usu.edu/~wang/cpam.pdfChanillo, Akshay Chanillo, Sagun and Maalaoui, Ali 2018. *Norm constants* in *cases* of the Caffarelli–Kohn–Nirenberg *inequality*. Pacific Journal of ...

https://www.cambridge.org/core/journals/proceedings-inequalities (i.e., 0 < a < 1 and at least one of s,µ,θ is nonzero), see the review paper by Dolbeault and Esteban [15]. Compared with the special cases of the Gagliardo-Nirenberg inequalities without the interpolation term (i.e., a = 1), dealing with such CKN inequalities encounters considerably more diﬃculty.

https://arxiv.org/pdf/1510.01224.pdfSome of our results were obtained earlier by Lam and Lu. Our proofs are radical simplifications of earlier proofs. In the case $\alpha>0$ we establish that we have symmetry breaking and optimizers to the CKN inequalities do not exist. This case was not treated by Lam and Lu. Our results thus are in the full parameter range of \alpha.

https://arxiv.org/abs/1701.00901Some of our results were obtained earlier by Lam and Lu. Our proofs are radical simplifications of earlier proofs. In the case $\alpha>0$ we establish that we have symmetry breaking and optimizers to the CKN inequalities do not exist. This case was not treated by Lam and Lu. Our results thus are in the full parameter range of \alpha.

http://adsabs.harvard.edu/abs/2017arXiv170100901CA subset of Caffarelli–Kohn–Nirenberg *inequalities* ... Similar *inequalities* in the Euclidean *case* are a subset of the celebrated ... by the LN-*norm* of its

https://link.springer.com/content/pdf/10.1007/s10231-017-0650-7.pdf- Norm Constants in cases of the Caffarelli-Kohn-Nirenberg inequality
- Sharp Constants
- Caffarelli–Kohn–Nirenberg Inequality
- ANISOTROPIC L2-WEIGHTED HARDY AND L2-CAFFARELLI
- Extended Caffarelli–Kohn–Nirenberg inequalities and superweights
- Extremal functions for Caffarelli-Kohn-Nirenberg and logarithmic
- Results on Parabolic Equations Related to Some Caffarelli-Kohn
- A scaling approach to Caffarelli-Kohn-Nirenberg inequality
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