Hopf's lemma for viscosity solutions to a class of non-local equations with applications

被引：10

作者：

Biswas, Anup ^{[1
]}

Lorinczi, Jozsef ^{[2
]}

机构：

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

[2] Loughborough Univ, Dept Math Sci, Loughborough LE11 3TU, Leics, England

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2021年 / 204卷

关键词：

Bernstein functions of the Laplacian; Non-local Dirichlet problem; Principal eigenvalue problem; Hopf's lemma; Moving planes; Overdetermined torsion equation; Subordinate Brownian motion; Ascending ladder height process; STRONG MAXIMUM PRINCIPLE; OVERDETERMINED PROBLEMS; FRACTIONAL LAPLACIANS; NONLINEAR EQUATIONS; SYMMETRY; REGULARITY; OPERATORS; EXTERIOR; EIGENFUNCTIONS;

D O I：

10.1016/j.na.2020.112194

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a large family of integro-differential equations and establish a nonlocal counterpart of Hopf's lemma, directly expressed in terms of the symbol of the operator. As closely related problems, we also obtain a variety of maximum principles for viscosity solutions. In our approach we combine direct analysis with functional integration, allowing a robust control around the boundary of the domain, and make use of the related ascending ladder height-processes. We then apply these results to a study of principal eigenvalue problems, the radial symmetry of the positive solutions, and the overdetermined non-local torsion equation. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：18

共 53 条

[1] Concentrating solutions for a class of nonlinear fractional Schrodinger equations in RN [J].