Analysis Seminar

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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.

Synopsis:

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.