On overdetermined problems for a general class of nonlocal operators

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Biswas, Anup¹  Jarohs, Sven² 

[1] Indian Inst Sci Educ & Res, Dept Math, Dr Homi Bhabha Rd, Pune 411008, Maharashtra, India

[2] Goethe Univ Frankfurt, Inst Math, Robert Mayer Str 10, D-60054 Frankfurt, Germany

关键词: Viscosity solutions;    Moving plane;    Subordinate Brownian motions;    Hopf's Lemma;    Rigidity result;   

DOI  :  10.1016/j.jde.2019.09.010

来源: Elsevier

【 摘 要 】

We study the overdetermined problem for a large family of non-local operators given by generators of subordinate Brownian motions. In particular, this family includes the fractional Laplacian, relativistic stable operators etc. We consider these problems in bounded domains, exterior domains, and in annular domains and we show that under suitable conditions, the domains and solutions are both radially symmetric. Our method uses both analytic and probabilistic tools. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free