Reifenberg平面域上非局部椭圆方程的边界正则性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-08-02 DOI:10.1016/j.na.2025.113908

Adriano Prade

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引用次数: 0

摘要

证明了一类非局部椭圆方程解的尖锐边界正则性，这些解由可与分数阶拉普拉斯算子相比较的算子在Reifenberg平面上产生，且具有零外部条件。更准确地说，如果算子的阶数是2s，那么在平面度参数足够小的情况下，对于所有的ε >；0，解都是Cs−ε正则的。这种证明依赖于归纳论证，其主要成分是适当障碍的构建和比较原则。

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Boundary regularity for nonlocal elliptic equations over Reifenberg flat domains

We prove sharp boundary regularity of solutions to nonlocal elliptic equations arising from operators comparable to the fractional Laplacian over Reifenberg flat sets and with null exterior condition. More precisely, if the operator has order

2 s

then the solution is

C^{s - ɛ}

regular for all

ɛ > 0

provided the flatness parameter is small enough. The proof relies on an induction argument and its main ingredients are the construction of a suitable barrier and the comparison principle.

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来源期刊

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.