Optimal Hardy inequalities on graphs

The talk is devoted to sharp Hardy inequalities for Laplace (type) operators on weighted graphs. We give sufficient criteria for the existence of Hardy weights in terms of positive superharmonic functions. The method is based on a discrete version of the supersolution construction which has been studied before in the context of elliptic Schrödinger operators on continuous spaces. We also intend to shed some light on optimality criteria and say a word or two about the proofs.

Joint work with Matthias Keller and Yehuda Pinchover.