Segregated configurations involving the square root of the laplacian and their free boundaries

Daniela De Silva, Susanna Terracini

Published 2018-10-03Version 1

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 resultsfor the standard diffusion to some anomalous case.