Critical Dipoles in Dimensions n ≥ 3
Access rightsNo access - Contact email@example.com
MetadataShow full item record
We consider generalizations of Hardy's inequality corresponding to the case of (point) dipole potentials in three or more spatial dimensions. More precisely, we prove the existence of a critical dipole coupling constant γ>0 such that a Hardy-type inequality holds for infinitely differentiable functions which are compactly supported in n-dimensional Euclidean space away from the origin. This coupling constant is optimal, that is, the largest possible such constant, and we discuss a numerical scheme for its computation. The quadratic form inequality will be a consequence of the fact that the L2-closure of the dipole operator is bounded from below by zero if and only if the coupling constant ranges from 0 to the critical γ.