Talk by Patricia Alonso Ruiz
On May 15th, 2024, Patricia Alonso Ruiz (Texas A&M) gave a talk about "Where could p-energies come from? On a quest to find them in Cheeger spaces" as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.
Abstract
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The classical p-energy is a functional that arises by integration of the pth power of the gradient. It is associated with a non-linear operator, the p-Laplacian, that serves as the basis of many problems in PDE. Being defined in terms of a gradient, one runs into trouble when the underlying space has no straightforward notion of the latter. Can we make sure that there is still a natural notion of p-energy in the absence of a gradient?
Motivated by that question, we discuss in this talk a way to construct a p-energy in the framework of Cheeger spaces without involving their differential structure. Instead, we will exploit the characteristic features of a Cheeger metric measure space: The doubling property and a (p, p)-Poincaré inequality for Lipschitz functions.
The talk is based on joint work with Fabrice Baudoin.
