EVENT DETAILS AND ABSTRACT

Title: Weak harmonic map flows with singular targets
Speaker: Stanley Snelson
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

We discuss heat flow constructions from Euclidean domains into non-smooth spaces. First, we describe a nonlocal constrained heat flow into a metric tree, which was originally motivated by a stationary eigenvalue partition problem. We prove spatial Lipschitz continuity and free interface regularity, and characterize the limit of the flow as time goes to infinity as a stationary solution of the partition problem. Next, we discuss ongoing work regarding the extension of this study to non-constrained heat flows into F-connected simplicial complexes, which are natural generalizations of trees to higher dimensions.