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

2018/08/06 by Sire, Yannick, Terracini, Susanna, Tortone, Giorgio · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.01851

Abstract

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 L_a = div(\absy^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 \citefkj,fjk2,fks 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 \citeCS2007. 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 \citeMR1010169,MR1305956,MR1090434.

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