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in the (a,b) plane, the rotational symmetry of the optimizers is broken. A more detailed analysis by Felli and Schneider [8] shows that the region where the optimiz-ers have a broken symmetry contains the set RFS:= {(a,b) : a < 0, b < bFS(a)} where bFS(a) := d(ac −a) 2 p (ac −a)2 +d−1 +a −ac. We call this region RFS the Felli-Schneider region.

https://hal.archives-ouvertes.fr/hal-01286546/documentAbstract: 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/1603.03574investigate 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-... Optimal *Symmetry* Results for the *Optimizers* of Caffarelli-*Kohn*-Nirenberg ... proving the radial *symmetry* of the *optimizers* of Caffarelli-*Kohn* ...

http://bicmr.pku.edu.cn/content/show/18-1511.html?catid=KiQhKyYsAbstract 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 optimizers for the inequalities have broken symmetry. It has been shown recently that in the complement of this region the optimizers are radially symmetric.

http://adsabs.harvard.edu/abs/2016arXiv160303574DIn 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-01286546We use the formalism of the Rényi entropies to establish the *symmetry* range of extremal functions in a family of subcritical Caffarelli–Kohn–Nirenberg ...

https://www.sciencedirect.com/science/article/pii/S1631073X17300043In 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://www.researchgate.net/publication/301842499_CAFFARELLI-*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.pdfMaria J. Esteban of Paris Dauphine *University,* Paris UPD with ... for Research in Decision Mathematics; ... and *symmetry* of Caffarelli-*Kohn*-Nirenberg and ...

https://www.researchgate.net/profile/Maria_Esteban2- Symmetry of optimizers of the Caffarelli-Kohn-Nirenberg inequalities
- On the Caffarelli‐Kohn‐Nirenberg inequalities
- SYMMETRY AND NONLINEAR DIFFUSION FLOWS 1
- Recent Applications of Nirenberg's Classical Ideas
- Consider the following inequalities due to Caffarelli
- Kohn
- and Nirenberg
- and the symmetry properties of minimizers
- we establish radiality of optimizers in some
- Caffarelli–Kohn–Nirenberg inequalities