The nodal set of solutions to anomalous equations

Bruno Pini Mathematical Analysis Seminar

Giorgio Tortone¹ 

[1] Dipartimento di Matematica, Alma Mater Studiorum Università di Bologna;

关键词: nodal set;    degenerate or singular elliptic equations;    nonlocal diffusion;    monotonicity formulas;    blow-up classification;   

DOI  :  10.6092/issn.2240-2829/10367

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown