The nodal set of solutions to anomalous equations

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 A2, these operators appear in the seminal works of Fabes, Kenig, Jerison and Serapioni [FKS82, FKJ83, FJK82]. 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 [HS89, Han94, Lin91].