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

Autor: Giorgio Tortone, Susanna Terracini, Yannick Sire
Rok vydání: 2018
Předmět:
DOI: 10.48550/arxiv.1808.01851
Popis: 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 ( | y | a ∇ ) , with a ∈ ( − 1 , 1 ) and their perturbations. As they belong to the Muckenhoupt class A 2 , these operators appear in the seminal works of Fabes, Kenig, Jerison and Serapioni [1] , [2] , [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] , [6] , [7] .
Databáze: OpenAIRE