Robustness for a Liouville Type Theorem in Exterior Domains

被引：6

作者：

Bouhours, Juliette ^{[1
,2
]}

机构：

[1] Univ Paris 06, Sorbonne Univ, Lab Jacques Louis Lions, UMR 7598, F-75005 Paris 05, France

[2] CNRS, Lab Jacques Louis Lions, UMR 7598, F-75005 Paris, France

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2015年 / 27卷 / 02期

关键词：

Elliptic equation; Liouville type result; Obstacle; Maximum principle;

D O I：

10.1007/s10884-014-9368-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are interested in the robustness of a Liouville type theorem for a reaction diffusion equation in exterior domains. Indeed Berestycki et al. (Commun. Pure Appl. Math., 62(6):729-788, 2009) proved such a result as soon as the domain satisfies some geometric properties. We investigate here whether their result holds for perturbations of the domain. We prove that as soon as our perturbation is close to the initial domain in the topology the result remains true while it does not if the perturbation is not smooth enough.

引用

页码：297 / 306

页数：10