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In their simplest form, the Caffarelli-Kohn-Nirenberg inequalities are a two parameter family of inequalities. It has been known that there is a region in parameter space where the …

https://www.researchgate.net/publication/301842499_Abstract: In their simplest form, the Caffarelli-*Kohn*-Nirenberg inequalities are a two parameter family of inequalities. It has been known that there is a ...

https://arxiv.org/abs/1603.03574In this talk I will present recent results, obtained in collaboration with J. Dolbeault and M. Loss, proving the radial symmetry of the optimizers of Caffarelli-Kohn-Nirenberg inequalities whenever they are local minima in the full functional space. These results are optimal and close a series of works proving partial results.

http://www.pku.org.cn/?p=20915F. Catrina and Z.-Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions, Comm. Pure Appl. Math. 54 (2001), no. 2, 229–258.

https://www.projecteuclid.org/download/pdf_1/euclid.pja/1459516319CAFFARELLI-*KOHN*-NIRENBERG INEQUALITIES NGUYEN LAM AND GUOZHEN LU ... Actually, the problem of *symmetry* and *symmetry* breaking of *optimizers* for the CKN

https://arxiv.org/pdf/1510.01224.pdfAbstract In their simplest form, the Caffarelli-*Kohn*-Nirenberg inequalities are a two parameter family of inequalities. It has been known that there is a ...

http://adsabs.harvard.edu/abs/2016arXiv160303574DCAFFARELLI-KOHN-NIRENBERG INEQUALITIES 233 equation corresponding to (1.8). The two problems will be shown to be equivalent, and we shall mainly work on the transformed one on R SN−1. The advantage in working on the latter is that the equation is an autonomous one and is deﬁned in H1.R SN−1/.

http://www.math.usu.edu/~wang/cpam.pdfIn their simplest form, the Caffarelli-Kohn-Nirenberg inequalities are a two parameter family of inequalities. It has been known that there is a region in parameter space where the optimizers for the inequalities have broken symmetry. It has been shown recently that in the complement of this region the optimizers are radially symmetric.

https://hal.archives-ouvertes.fr/hal-01286546investigate 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/Norm-Constants-in-Cases-of-the-Caffarelli...- Symmetry of optimizers of the Caffarelli-Kohn-Nirenberg inequalities
- On the Caffarelli‐Kohn‐Nirenberg inequalities
- Symmetry for extremal functions in subcritical Caffarelli–Kohn
- On symmetric solutions of a critical semilinear elliptic system
- Recent Applications of Nirenberg's Classical Ideas
- Consider the following inequalities due to Caffarelli
- Kohn
- optimal symmetry properties for the optimizers of the Caffarelli–Kohn–Nirenberg inequalities
- if symmetry holds
- we establish radiality of optimizers in some Caffarelli-Kohn-Nirenberg