Symmetry results for viscosity solutions of fully nonlinear equations in annular and exterior domains

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:485

Article

Hao, Yuebin¹  Dai, Limei² 

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[2] Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R China

关键词: Radial symmetry;    Viscosity solutions;    Annular domains;    Exterior domains;    Moving plane method;   

DOI  :  10.1016/j.jmaa.2019.123776

来源: Elsevier

【 摘 要 】

In this paper, we prove the symmetry and monotonicity results of viscosity solutions for fully nonlinear elliptic equations F(D(2)u, Du, u, x) = 0 and fully nonlinear parabolic equations -u(t) + F(D(2)u, Du, u, x, t) = 0 in annular domains by using the method of moving planes. We also prove the symmetry and monotonicity results of viscosity solutions for fully nonlinear parabolic equations -ut + F(D(2)u, Du, u, t) = 0 in exterior domains. This extends the results of fully nonlinear elliptic equations in exterior domains. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free