M 511

The Hardy inequality stands in the core of mathematical physics as having a Hardy inequality is strongly connected to hyperbolic manifolds and graphs, transient jump processes and subcritical energy functionals. Thus, it connects geometry, probability theory and analysis in a certain sense. Besides studying the validity of the inequality, the discussion of the optimality of the corresponding weights is of main interest. In this talk, we introduce the corresponding quasi-linear setting on locally finite graphs and show a method to obtain optimal Hardy weights. We illustrate this method on various examples. Moreover, we show a decay condition for Hardy weights. If the time permits, we also discuss characterisations of having a Hardy inequality in the quasi-linear setting.

Dr. Florian Fischer

Bonn