6 problems

Radial symmetry conjecture. The extremal functions in $(\mathrm{cknrs})$ are radially symmetric if

Let $p$, $q$, $N$, and the parameters in the discrete Caffarelli–Kohn–Nirenberg and Gagliardo–Nirenberg settings be as in the paper. Consider the discrete $p$-Laplace Hardy equatio…

Symmetry-breaking conjecture. The only manner in which the symmetry of a global extremal can break is when the symmetric extremal function is linearly unstable; consequently, it ca…

Let $d$ and $p$ be as in the preceding symmetry results, and let $\theta$ be the interpolation parameter. Denote by $\Lambda_{\rm s}(\theta,p,d)$ the symmetry threshold and by…

Threshold equality conjecture. The condition

Threshold coincidence conjecture. The functions $\Lambda^*$ and $\Lambda^{FS}$ coincide over the whole range