The nodal set of solutions to anomalous equations

Abstract

This note focuses on the geometric-theoretic analysis of the nodal set of solutions to specific degenerate or singular equations. As they belong to the Muckenhoupt class A_2, these operators appear in the seminal works of Fabes, Kenig, Jerison and Serapioni. In particular, they have recently attracted a lot of attention in the last decade due to their link to the local realization of the fractional Laplacian. The  goal is to get a glimpse of the complete theory of the nodal set of solutions of such equations in the spirit of the seminal works of Hardt, Simon, Han and Lin.