Title: Duality for the gradient of a p-harmonic function and the existence of gradient curves
Abstract: We consider p-harmonic functions on a metric measure space. They are defined as continuous minimizers of the p-energy functional. We discuss a duality argument that yields the existence of gradient curves for a p-harmonic function. Based on this insight, we present a simple example of a p-harmonic function u that does not satisfy "sheaf property". More precisely, u is p-harmonic in two domains separately, but not in their union. The talk is based on joint work with Sylvester Eriksson-Bique.
