A Dirichlet problem for nonlocal degenerate elliptic operators with internal nonlinearity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:448

Article

Yu, Hui¹ 

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

关键词: Nonlocal elliptic equations;    Degenerate elliptic equations;    Higher regularity;    Dirichlet problem;    Diffusion process;   

DOI  :  10.1016/j.jmaa.2016.11.005

来源: Elsevier

【 摘 要 】

We study a Dirichlet problem in the entire space for some nonlocal degenerate elliptic operators with internal nonlinearities. With very mild assumptions on the boundary datum, we prove existence and uniqueness of the solution in the viscosity sense. If we further assume uniform ellipticity then the solution is shown to be classical, and even smooth if both the operator and the boundary datum are smooth. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free