2 problems

Aharonov–Bohm Hardy conjecture. If $\beta\notin\mathbb{Z}$, then there exists a constant $\lambda(p)>\left(\frac{2-p}{p}\right)^p$ such that

Let $d\geq 2$, let $\nabla_A$ denote the magnetic gradient, let $h_{A,p}$ be the corresponding magnetic $p$-Laplacian form domain, and let $\mu_{p,d}$ be the Hardy constant. Let…