Segregated configurations involving the square root of the Laplacian and their free boundaries
Speaker: Susanna Terrancini
Location: Warren Weaver Hall 314
Date: Tuesday, November 20, 2018, 2 p.m.
We study the local structure and the regularity of free boundaries of segregated critical configurations involving the square root of the laplacian. We develop an improvement of flatness theory and, as a consequence of this and Almgren's monotonicity formula, we obtain partial regularity (up to a small dimensional set) of the nodal set, thus extending the known results by Caffarelli and Lin, Tavares and Terracini for the standard diffusion to some anomalous case. This is a joint work with Daniela De Silva.