The standard Euclidean p-energy form is a genuinely non-linear form whose associated operator, the p-Laplacian, serves as the basis of many problems in PDE. Being originally defined in terms of a gradient, the question arises: Would it be possible to construct a p-energy form without relying on the gradient?
Motivated by this question we will discuss a way to construct p-energy forms in the framework of Cheeger spaces without involving their differential structure. Instead, we will exploit characteristic features of Cheeger metric measure spaces such as the doubling property and the (p,p)-Poincaré inequality with respect to Lipschitz functions.
The talk is based on joint work with Fabrice Baudoin.