Speaker: Aleksis Koski, Aalto University

Title:The Trace Theorem for Sobolev Homeomorphisms

Abstract: Classical Sobolev trace theory tells us when a boundary map can be extended as a Sobolev function inside a given domain in R^n. For the purposes of minimization problems in Nonlinear Elasticity, it is natural to rephrase this question in the context of extending a given embedding of the boundary as a homeomorphic Sobolev map. In this talk, I will explain what is known about this problem, ending with a full trace theory for Sobolev homeomorphisms in 2D.

Speaker: Sylvester Eriksson-Bique, University of Jyv¨askyl¨a

Title: P-Dirichlet spaces and the resolution of the resistance and energy image density conjectures

Abstract: I will describe the resolution of two conjectures related to Dirichlet forms. In both cases a conceptually simple solution arises by stepping away from the p=2 regime. This leads to a new definition of a p-Dirichlet space, which unifies three quite different areas: Dirichlet form theory, Analysis on fractals and Analysis on metric spaces. The talk includes joint work with Mathav Murugan