On families of optimal Hardy-weights for linear second-order elliptic operators (Q2295691)

Given a nonnegative linear second order elliptic operator \(\mathcal{P}\), the authors contruct families of optimal (in the sense of criticality theory) Hardy-weights. The results generalize those of [\textit{B. Devyver} et al., J. Funct. Anal. 266, No. 7, 4422--4489 (2014; Zbl 1298.47057)]. In fact, a characterization of the set of all optimal Hardy weights in the one-dimensional case is provided first, and then a one-dimensional reduction argument is used to tackle the case for \(\mathcal{P}\).