The Dirichlet problem for nonlocal elliptic operators with 𝐶^{0,𝛼} exterior data,Proceedings of the American Mathematical Society

当前位置： X-MOL 学术 › Proc. Am. Math. Soc. › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

The Dirichlet problem for nonlocal elliptic operators with 𝐶^{0,𝛼} exterior data
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-07-20 , DOI: 10.1090/proc/15121
Alessandro Audrito , Xavier Ros-Oton

Abstract:In this note we study the boundary regularity of solutions to nonlocal Dirichlet problems of the form

in $\Omega$ ,

in $\mathbb{R}^N\setminus \Omega$ , in non-smooth domains $\Omega$ . When

is smooth enough, then it is easy to transform this problem into an homogeneous Dirichlet problem with a bounded right-hand side for which the boundary regularity is well understood. Here, we study the case in which $g\in C^{0,\alpha }$ , and establish the optimal Hölder regularity of

up to the boundary. Our results extend previous results of Grubb for $C^\infty$ domains $\Omega$ .

中文翻译：

具有𝐶^ {0，𝛼}外部数据的非局部椭圆算子的Dirichlet问题

摘要：在此，我们就解决边界规律性研究，以形式的非本地狄利克雷问题

在 $\ Omega$ ，

在，在非光滑域。如果足够光滑，则很容易将此问题转换为右边界有限的齐次Dirichlet问题，对此边界规则很容易理解。在这里，我们研究的情况，并建立直至边界的最佳Hölder正则性。我们的结果扩展了Grubb对于域的先前结果。 $\ mathbb {R} ^ N \ setminus \ Omega$ $\ Omega$

$g \ in C ^ {0，\ alpha}$

$C ^ \ infty$ $\ Omega$

更新日期：2020-09-01

点击分享查看原文

点击收藏

公开下载

阅读更多本刊最新论文本刊介绍/投稿指南

全部期刊列表>>