On the nodal set of solutions to degenerate or singular elliptic equations with an application to s-harmonic functions

This work is devoted to the geometric-theoretic analysis of the nodal set of solutions to degenerate or singular equations involving a class of operators including La=div(|y|a∇), with a∈(−1,1) and their perturbations. As they belong to the Muckenhoupt class A2, these operators appear in the seminal works of Fabes, Kenig, Jerison and Serapioni [1–3] and have recently attracted a lot of attention in the last decade due to their link to the localization of the fractional Laplacian via the extension in one more dimension [4]. Our goal in the present paper is to develop a complete theory of the stratification properties for the nodal set of solutions of such equations in the spirit of the seminal works of Hardt, Simon, Han and Lin [5–7].